1. The demand for wheat in a country is QD = 200 − 2P, and supply is QS = −20 + 2P, where P is price in pounds and Q is quantity in tonnes. (a) Find the no-trade equilibrium price and quantity in the market. What are the values of consumer and producer surplus in equilibrium? (b) The government decides to open the domestic market to imports. The world price of wheat is £20 per tonne. In order to safeguard farming the government sets a tariff of £20 per tonne. Illustrate on a diagram and calculate the government's revenue from the tariff. (c) Calculate the new consumer surplus and producer surplus under (b). By how much is society better off than under (a) above? Comment on the implications for the distribution of income between farmers and consumers if the tariff revenue is given to farmers as a lump sum payment. 2. Discuss the following questions and substantiate your arguments with economic theory. Clearly state which assumptions you make in answering the questions. Make use of diagrams where appropriate. (a) You are charged with maximising governmental revenues from cigarette taxation. What kind of tax rate do you propose and why? Is it possible that you would advise the government to reduce the tax rate? Why or why not? (b) Discuss possible reasons why a government that wants to increase tax revenues would like to tax cigarettes at all. Are there other goods you think that revenue-maximising governments would like to tax? Why? (c) How would your answer to (a) change if in addition to generating revenues, the government would also like to make people healthier? 3. In a perfectly competitive market, the demand curve is QD = 120 − 3P and the supply curve is QS = 2P, where QD is the quantity demanded, QS is the quantity supplied, and P is the price. 1(a) Find the equilibrium price and quantity. Calculate consumer and producer surplus in this market. (b) The government now introduces a tax of T = 10 per unit sold, so that the supply curve now becomes QS = 2(P − T), where P is the price paid by consumers. Calculate the government's revenue from the tax. (c) Find the deadweight loss associated with the tax. How else could the government in this example raise the same tax revenue, without incurring any deadweight loss? 4. In a competitive market, market demand is q d = 104 − 16p, where q d denotes the quantity demanded and p is the price. Market supply is q s = 8p − 16, where q s denotes the quantity supplied. (a) Explain why at the equilibrium it must be true that demand equals supply. Calculate the equilibrium price and quantity in the market. Show your result diagrammatically. (b) Explain the concepts of consumer and producer surplus. Use your results in (a) to calculate producer and consumer surplus in this economy. (c) Now suppose the government introduces a specific tax, t = 3 paid by the suppliers. Find the new equilibrium price and quantity in the market and compare your result to your result in (a). Show your result diagrammatically. (d) Using a diagram to illustrate your answer, explain how the introduction of a specific tax creates a deadweight loss in the market. Explain how this deadweight loss depends on the elasticity of demand. 5. Assume that the UK changes planning regulations to the extent that it becomes easier to build new houses. Making use of economic theory and diagrams where appropriate, discuss the effect of this regulatory change on the following: (a) The price of houses for first-time buyers. Clearly state any assumptions you make in your answer. (b) The demand for country houses adjacent to new housing developments. Clearly state any assumptions you make in your answer. (c) Does your answer to (b) depend on whether new houses are accompanied by better infrastructure (e.g., shops, road, schools, etc.)? Clearly state any assumptions you make in your answer. 6. Consider a consumer with utility function U(x, y) = 2x + y. The price of good x is px = 10, which is identical to the price of good y, py = 10. The total income of the consumer is given by M = 500. (a) Derive the Marginal Rate of Substitution between goods x and y and solve for the optimal consumption bundle. 2(b) Show the solution in a graph. What level of utility is the consumer going to achieve with this bundle? (c) Now assume that the price of good y decreases to 5. Find the new optimal consumption bundle and comment on it. (d) Find the income and substitution effects associated with the decrease in the price of y. Explain your finding. 7. Jim has an income of £100 which he spends on two goods, beer and pizza. The price of beer is £2 per unit and the price of pizza is £2 per unit. Assume that Jim behaves optimally. (a) Write down Jim's budget constraint. Draw a diagram of Jim's budget line with pizza on the horizontal axis. Jim consumes 30 pizzas. How many beers does he consume? (b) Now the price of pizza falls to £1 per unit and Jim consumes 50 pizzas. The price of beer and Jim's income are unchanged. Jim tells us that with the pizza price at £1 he would be just as well off as he was originally (under (a) above) if he had an income of £70, in which case he would consume 40 pizzas. Use this information to calculate the substitution and income effects of the fall in the price of pizza from £2 to £1. (c) Is beer a normal good for Jim? Explain. 8. John's utility function is given as: U(x, y) = xy, where x and y denote the quantities of goods x and y he consumes. His budget constraint is: 4x + 8y = 120, where 4 is the price of good x, 8 is the price of good y and 120 is his income. (a) From the utility function find the expression of the Marginal Rate of Substitution for John. Find the typical equation of an Indifference Curve for John. (b) Find the optimal quantities for x and y consumed by John. Show your solution diagrammatically. (c) John's friend Anne has exactly the same income as John. However, Anne's utility function is U(x, y) = x 1 3 y 2 3 . Find the equation of Anne's Marginal Rate of Substitution and her optimal consumption bundle. (d) Compare the optimal bundles of John and Anne. Discuss. 9. Discuss the following statements making use of consumer theory. In your answers, clearly state any assumptions you make and substantiate your claims with economic theory. Make use of diagrams where appropriate. (a) Consumer theory cannot explain why water is cheaper than diamonds, because obviously people get much more utility from water than from diamonds. (b) You observe a consumer who invests part of his savings into a safe asset with a fixed return of 4% and part into a risky asset that gives him either 0% or 10% return with equal probability. If the returns of the risky asset increase to 2% and 12% (with equal probability) respectively, you will observe that the consumer now chooses to invest more in the risky asset than before. 310. Consider a perfectly competitive market for a given good. Assume that the market demand is given by q D = 210 − 3p, where q D is the quantity demanded and p is the price. The market supply is q S = −10 + 2p, where q S is the quantity supplied. (a) Find the equilibrium price and quantity in the market. Show the equilibrium in a graph by plotting the inverse demand and supply functions. (b) Explain the concepts of producer and consumer surplus. Using your results in part (a), calculate the consumers' surplus, the producers' surplus and total surplus in the economy. (c) Now assume that the government introduces a price cap in the market of p cap = 30. Find the new equilibrium quantities supplied and demanded under this price cap, as well as consumer, producer, and total surplus. Show your result graphically. (d) Compare your result in (c) with your result in (b) and use this comparison to evaluate the introduction on the price cap. 11. Consider a competitive market for a given good. The market demand is: q D = 20 − 2p, while the market supply is: q S = 3p − 5. (a) Find the equilibrium price and the equilibrium quantity. Sketch the equilibrium in a diagram. (b) Now suppose that the government introduces a specific tax t = 2.5 in the market. Find the new equilibrium price and quantity after the tax is introduced. Show in a diagram the effects on the market equilibrium of introducing such a tax. (c) Assume that demand instead is given by: q D = 15 − p. The market supply is as before. Show that the equilibrium values of price and quantity before the introduction of the tax are as in (a), but that the equilibrium values after the tax introduction are not. Explain. (d) Discuss the incidence of the tax under the two demand functions. 12. John earns £4 per hour and he has no non-labour income. He decides to work 30 hours per week. (a) Show John's utility maximising choice of leisure and his weekly income on a diagram. (b) Now the government introduces a welfare system that provides a minimum lump-sum income of £80 per week. Draw John's new budget line. Assuming that leisure is a normal good, will John work fewer hours under the welfare system? Explain. (c) Instead of the lump-sum payment in (b), the government offers John an extra 50p per hour worked. Draw the new budget constraint. Assuming again that leisure is a normal good, will John work more or less than 30 hours per week? Explain. 13. Are the following statements true or false? In each case, explain why they are true / false and discuss the impact of monetary and fiscal policy. Use diagrams and equations wherever it helps your arguments. 4(a) If investment is not very sensitive to the interest rate, the IS curve is almost vertical. (b) If money demand is not very sensitive to the interest rate, the LM curve is almost vertical. (c) If the money demand is extremely sensitive to the interest rate, the LM curve is horizontal. 14. Assume that the domestic demand for a good is QD = 100 − P, and domestic supply is given by QS = 40 + P. The market for this good is perfectly competitive. (a) Assume that the economy is closed. Calculate equilibrium price and quantity and show them in a graph. (b) Assume that the economy opens to trade and that the world price for this good is £50. What are the equilibrium price and quantity in the domestic market? Show them in a graph. (c) Calculate the consumer and the producer surplus in both (a) and (b). Compare them and discuss your findings, with special reference to whether it is beneficial for the country to open to trade. 15. Consider the following economy. Consumption, C, depends on income, Y , and private investment, I, is exogenous. There is no government: C = 100 + 0.7Y I = 40 This is an open economy, where imports, Z, increase with national income. Assume also that exports, X, increase with the national income, Y X, of the home country's trading partner (the home country takes Y X as given): Z = 10 + 0.1Y X = 10 + 0.1Y X (a) Write down the aggregate demand function for this economy and graph it in the Keynesian Cross. (b) What is the equilibrium income of this economy? What value does it take if Y X = 100? (c) Assume now that exports are described by X = 10 + 0.2Y X. Everything else remains unchanged. Calculate the new equilibrium income. How does this change affect the multiplier? Explain. 16. The following questions deal with the IS − LM model of a closed economy and the concept of a "liquidity trap": 5(a) A liquidity trap is a scenario in which interest rates are very close to zero. Within the IS−LM model in which the nominal interest rate is equal to the real interest rate, discuss how such low interest rates relate to the willingness of people to hold money and to the elasticity of the LM curve. Draw the IS − LM equilibrium of an economy that is in a liquidity trap. (b) Discuss the relative effectiveness of fiscal vs. monetary policy for a country in a liquidity trap. Make use of relevant diagrams in your answer. (c) In reality, nominal and real interest rates tend to differ by the rate of inflation, π, such that i = r + π, where i is the nominal interest rate and r the real interest rate. On which of these interest rates should money demand principally depend on? How does this impact the existence of a liquidity trap and the effectiveness of monetary policy? 17. Discuss the following statements within a Keynesian cross model. Make use of economic theory to substantiate your claims. (a) In a closed economy where the private sector invests more that it saves, the government must be running a budget deficit. (b) To increase economic income in an open economy, the government should ban imports. (c) The government budget multiplier is bigger in a closed economy than in an open economy. 18. Consider the following model: C = C0 + c(Y − T), I = I0 − br, where C is consumption, I investment, Y is income and T denotes lump sum taxes. C0 > 0 and I0 > 0 are autonomous consumption and investment respectively, 0 < c < 1 is the marginal propensity to consume out of disposable income, and b > 0 is sensitivity of investment with respect to the real interest rate (r). Denote government spending as G and assume that money demand is give by:  M P d = k(Y − T) − hr, where k > 0 and h > 0. Using the IS − LM model, show and discuss how the inclusion of T into the money demand function will affect the following: (a) Derive the equilibrium levels of income and interest rate in this economy. 6(b) If taxes were not included in the money demand function, ceteris paribus, equilibrium income and interest rate would be: Y ∗ = h bk + (1 − c)h  C0 + I0 + G + b h M P − cT r ∗ = k bk + (1 − c)h [C0 + I0 + G − cT] − 1 − c bk + (1 − c)h M P . With this information, and your result in (a), discuss how the inclusion of taxes in the money demand function affect the analysis of changes in government expenditure and taxes. 19. Answer the following questions within a Keynesian Cross model. In your answer, make use of economic theory and state clearly any assumptions you make along the way. (a) If the household saving rate in the UK was zero, what would be the impact of an increase in government spending? (b) How does your answer to (a) change if the UK had a large trade deficit with the rest of the world? (c) How do your answers to (a) and (b) depend on how the UK raises tax revenues? In particular, does it matter whether the UK raises lump sum taxes, or proportional income taxes? 20. An economy is described by the following relationships: C = c0 + b(Y − T) I = I G = G T = T where C is consumption, I is investment, T are lump sum taxes, G is government spending, c0 is autonomous consumption, b is the marginal propensity to consume and Y is income. (a) Derive the equation for equilibrium income, Y ∗ . What is the government multiplier, i.e., the multiplier that shows by how much equilibrium income changes if government spending increases by 1 unit? (b) Explain why the government multiplier is bigger than 1. (c) Derive the tax multiplier in this economy, i.e., the multiplier that shows by how much equilibrium income changes if taxes increase by one unit. (d) Discuss the relative sizes of the multipliers you derived in parts (a) and (c). What do they imply for the effectiveness of government spending relative to taxation?