1. Suppose the demand curve for a good is given by the equation P = 200 - 1/2 Q and the supply curve is given by the equation P = 50 + 1/4 Q, where P represents the price of the good (measured in dollars per unit) and Q represents the quantity of the good (measured in units per week).
(i) Find the equilibrium price and quantity for this market.
(ii) Suppose quantity demanded for the good rises by 10 units at every possible price while at the same time quantity supplied rises by 5 units at every possible price. Find the new equilibrium price and quantity in this market.
(iii) Given the change in demand, how large would the rise in supply need to be (given the same 10 unit rise in demand) in order for the price to decrease instead of increasing as in part (iii)?
(iv) Suppose the government imposes a sales tax of $9 per unit on this good. Find the new formula for the demand curve, the new equilibrium quantity, the posttax price received by suppliers, and the post-tax price paid by demanders.
2. 2. Mathew has the utility function U =√XY (where Y represents apples and X represents hot dogs), income of $20, and is deciding how to allocate that income between apples and hot dogs. Both hot dogs and apples cost $1.00 each.
(i) Write the equation for Mathew's budget line in slope, intercept form (y = mx + c).
(ii) Mathew's utility function implies that the marginal utility of apples is 0.5√X/Y and the marginal utility of hotdogs is 0.5√Y/X . How many apples will Mathew buy? How many hot dogs will he buy?
(iii) This year, the price of hot dogs rise to $3 each while Mathew's income isunchanged. Mathew's father decides to help him by giving him a gift of $20.
Consider an indifference curve-budget line diagram with hot dogs on the x-axis and apples on the y-axis. After Mathew gets the $20 gift, will his new budget line lie above, lie below, or pass through his initial optimum? Justify your choice. Will Mathew be better or worse off than he was last year?
3. Suppose you have 24 hours per day that you can allocate between leisure and working at a wage rate of $2 per hour.
(i) Draw the budget constraint between "leisure hours" on the horizontal axis and "wage income" on the vertical. Show an optimum point A.
(ii) Draw your new budget constraint when the wage rate rises to $3 per hour. Show your new optimum point B.
(iii) On your indifference curve diagram, decompose the effect of the wage increase into a "substitution effect" and an "income effect". What is the direction of the substitution effect (that is, what happens to leisure/work)? What is the direction of the income effect if leisure is a "normal good"? What can you say about the "net effect" of the wage increase on your leisure choice?
4. You are an economist for the City Subway Commission. Presently, the price of a subway ride is 80¢, and 250,000 seats are filled weekly. The price elasticity of demand for subway rides is -0.40, and the income elasticity of demand is -0.60.
(i) If a recession lowered area incomes by 5%, how many additional seats per week would the subway need?
(ii) The Commission has just approved a subway price increase of 10¢ per ride. As a result, will the Commission's total revenue from subway rides rise or fall?
5. A firm is considering entering a market where demand for its product is Q = 100 - P. This demand function implies that the firm's marginal revenue function is MR = 100 - 2Q. The firm's total cost of producing the product for that market is TC = 1000 + 10Q + Q2 which indicates that its marginal cost function is MC = 10 + 2Q. Calculate the firm's profit and hence indicate whether or not the firm should enter the market.
6. The manager of a firm receives an engineering report claiming that an additional hour of capital would add twice as much output as would an additional hour of labor (Think MRTS!). According to the firm's accountants, an hour of capital costs 3 times more than an hour of labor.
(i) Is the firm on its expansion path? Why or why not?
(ii) If the firm is under contractual obligations to keep its output at current levels, what long-run adjustment (if any) should the manager make in the firm's employment of labor and capital? Demonstrate using an isoquant-isocost diagram. Label the initial situation "A" and the post-adjustment situation "B."