1) Sally has three possible bundles she can choose between: a) 2 oranges, 3 apples and 2 bananas b) 4 oranges, 4 apples and 3 bananas c) 1 orange, 5 apples and 4 bananas She is a rational consumer (her preferences satisfy the axioms of rational choice), and all three goods are 'goods' (i.e. she likes oranges, apples and bananas). Additionally we know that she prefers bundle c. to bundle b. Fill in the remaining preference relations: Bundle Relation Bundle Reason (axiom) Given: c b Given in question i. a b ii. c a 2) Bob only gets utility if he consumes his coffee with one unit of milk for every two shots of espresso. A shot of espresso is $2, and a unit of milk is $1. a) Write out a utility function for Bob representative of his preferences b) If his income is $15 what is his optimal bundle? Suppose the price of espresso falls to $1. c) What will his optimal bundle be now? Is there a substitution effect for espresso from the fall in price? 3) Timothy's utility function is . a) Find his demand for x and y as a function of income and prices x(p,I),y(p,I) For questions b)-c) Assume I=90, , b) Find Timothy's demand curve for good x, and plot on a graph c) Show on a graph the effect of an increase in income on consumption of both x and y using the income consumption curve. Is x an inferior good or a normal good?. 4) Jinny's Jumpers producers jumpers using wool (W) and labour (L). Her production function is . Wool costs $5/unit while labour costs $20 per unit. [please put L on the x-axis and W on the y-axis] a) Find her cost-minimizing bundle of wool and labour if she wants to produce 6 units. Show on a graph with the isocost and isoquant curves. b) Suppose the cost of labour decreases to $10 per unit, Explain using a graph how her optimal input bundle will change. [you don't need to find the new optimal bundle, just show the change on a graph] c) Suppose now that the cost of labour and wool both increase by 50% (from the original $5 and $20). Explain what effect this will have on the optimal input bundle, and why. Macroeconomics Question 1 (a) In an economy with flexible prices, competitive factor markets and fixed supplies of the factors of production, graphically illustrate the impact of a change in immigration policy that causes a huge outflow of workers to other countries, ceteris paribus. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curve's shift; and v. the terminal equilibrium values. Explain in words how the equilibrium values of labour, the real wage, saving, investment, and the real interest rate change. (b) In an economy with flexible prices, competitive factor markets, and fixed supplies of the factors of production, graphically illustrate the impact of a deadly virus that kills a large part of the labour force, but leaves the other factors of production untouched, ceteris paribus. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curves shift; and v. the terminal equilibrium values. Explain in words how the equilibrium values change. (c) Consider a production function for an economy: Y = AK0.5L0.4N0.1, where L is labour, K is capital, and N is land. In this economy the factors of production are in fixed supply with L = 100, K = 100, and N = 100. a. What is the level of output in this country? b. Does this production function exhibit constant returns to scale. Demonstrate by example. c. If the economy is competitive so that factors of production are paid the value of their marginal products, what is the share of total income will go to land? Question 2 (a) Assume that a country's production function is Y = AK0.3L0.7. The ratio of capital to output is 3, the growth rate of output is 3 percent, and the depreciation rate is 4 percent. Capital is paid its marginal product. i. What is the marginal product of capital in this situation? (Hint: The marginal product of capital may be computed using calculus by differentiating the production function and using the capital–output ratio or by using the fact that capital's share equals MPK multiplied by K divided by Y.) ii. If the economy is in a steady state, what must be the saving rate? (Hint: The saving rate multiplied by Y must provide for gross growth of ( + n + g)K, where  is the depreciation rate.) iii. If the economy decides to achieve the Golden Rule level of capital and actually reaches it, what will be the marginal product of capital? iv. What must the saving rate be to achieve the Golden Rule level of capital? (b) What is the Solow residual? Compare Prescott's interpretation of the fluctuations of the Solow residual over the business cycle with more standard explanations of these fluctuations. (c) Explain how the Solow growth model differs from models of endogenous growth with respect to: i. the sources of technological progress. ii. returns to capital. (d) It rains so much in the country of Tropicana that capital equipment rusts out (depreciates) at a much faster rate than it does in the country of Sahara. If the countries are otherwise identical, in which country will the Golden Rule level of capital per worker be higher? Illustrate graphically.