Consider the following demand and supply equations for beer: QD =140?2P

QS =20+P

7a) Find the equilibrium price and quantity of beer.

7b) What is the price elasticity of demand in equilibrium?

Now suppose the price of barley, an input in beer production, falls and hence the supply of beer shifts to:

QS =30+P

7c) What is the new equilibrium price and quantity of beer?

7d) What is the price elasticity of demand at this equilibrium?

7e) In which equilibrium, 7a or 7c, is demand relatively more elastic?

Suppose a small Island nation imports sugar for its population at the world price of $1,500 per ton, The domestic market for sugar Is shown below 2500 2000 1500 5 - World price Price (5/ton) 1000 Domestic price with subsidy 500 12 16 20 Quantity (tons/day) If the government provides a subsidy of $500 per ton, then the cost of subsidy, which must be borne by taxpayers, will be per day.1. Sarah consumes only two goods, which can be divided into fractions: ap ples (:31) and books (.132). Assume the price of books is p2 = 1. Suppose you know that, if she consumes 5 books, she can buy at most 10 apples. And if she consumes 8 books, she can buy at most 4 apples. (3) (b) (C) (d) Determine her income (m) and the price of apples (p1). Write out the equation of her budget line. Draw this on a graph (clearly marking the axes and intercepts) and indicate her budget set. Suppose the government taxes Sarahls apple consumption in the fol- lowing way: for each apple consumed, Sarah must pay a tax of t = %. Write out the equation for her new budget line, and draw it on a graph. After evaluating this policy, the government decides that the tax is too harsh. It now declares that the tax will kick in only after 5 apples. (If 1:1 <_c there is no tax. but if> 5, the tax applies to each apple that exceeds this cutoff.) Sarah will now face a kinked budget line. Write the equations corresponding to each part of her budget line, and draw them on a graph (indicate the bundle at which the kink occurs). This government is extremely indecisive. In another change of policy, it decides that the tax break makes sense for the poor, but there is no reason to oer it to the rich. The new policy is as follows: if a person's income is less than or equal to $10, she gets the tax break (as described in part c), but if her income is greater than $10, she must pay taxes on her entire purchase of apples (as described in part b). Now suppose Sarah's employer offers her a raise of $2. Can we be certain that Sarah will accept the raise? What about a raise of $4? Analyze this by thinking about how the budget set changes after each ralse. Problem set 1: Preferences and Utility Exercise 1: Suppose the utility function for two goods, X and Y, has the Cobb-Douglas form utility= U(X, Y) = VX . Y. a. Graph the U = 10 indifference curve associated with this utility function. b. If X = 5, what must Y equal to be on the U = 10 indifference curve? What is the MRS at this point? c. In general, develop an expression for the MRS for this utility function. Show how this can be interpreted as the ratio of the marginal utilities for X and Y. d. Consider a logarithmic transformation of this utility function: U' = log U where log is the logarithmic function to base 10. Show that for this transformation the U' = 1 indifference curve has the same properties as the U' = 10 curve calculated in part (a) and (b). What is the general expression for the MRS of this transformed utility function? Exercise 2: Graph a typical indifference curve for the following utility functions and determine whether they have convex indifference curves (that is, whether they obey the assumption of diminishing MRS): a. U = 3X + Y. b. U = VX . Y. c. U = VX2 + Yz. d. U = vx2 _ yz e. U = X2/3p1/3 f. U = log* + logY. Exercise 3: Consider the following utility functions: a. U(X, Y) = XY. b. U(X, Y ) = x2yz c. U(X, Y) = InX + InY. Show that each of these has a diminishing MRS, but that they exhibit constant, increasing, and decreasing marginal utility, respectively. What do you conclude