Answer these problems.
3. The market illustrated below has Inverse demand p(Q) = 130 - 30 and industry wide marginal cost MC(Q) = 10 + 2Q. If production is competitive, this is the market (inverse) supply curve. If production is consolidated under a monopolist, this is the monopolist's MC curve. a. Suppose there is a monopolist. Explain how marginal revenue for a monopolist is different than for a firm under perfect competition. Then derive the profit-maximizing market outcome (including the monopoly price and quantity @. and P.)- b. Now suppose the market operates under perfect competition, but with a per unit taxt = $30. Determine the market equilibrium and illustrate on a diagram. As a follow-up, determine the relationship Q (t) that gives the equilibrium market quantity as a function of the tax rate. c. If you invert the relationship from part (b), you have T(Q), the tax the government would need to set if it wishes the market quantity to be Q. Then total tax revenue is T(Q) = (Q) . Q. [This may be useful for the intuition that's requested below.I Determine whether total welfare in this market is higher (i) under a monopoly, or (fi) under perfect competition with an "empire-building" government that maximizes total tax revenue T'(Q). For (il), make the usual assumption that tax revenue is spent on something useful (le.. not wasted). Illustrate both cases on a single diagram, Do your best to explain why your comparison turns out as it does. [Applying intuition about the components of marginal revenue MR(Q) to the "marginal tax revenue" 7"(Q) might be helpful.] P P(Q) = 130 - 30 MC(Q) = 10 + 2Q (s(p) = 4p -5)Firm Optimization 6. (8 points) Suppose a firm uses capital (X), labor (Z), and energy (E) to produce output (). In the short-run, the firm cannot adjust its capital stock. The price of capital is r. price of labor is w, and the price of energy is e. The price of final output is p. In the short-run profit maximization problem, which of the variables K. L. E. O. p, r, w, e are exogenous? 7. (10 points) Assume a firm has the production function is Q=KL . To maximize the firm's profit, it satisfies the condition w = pMPL. In the short-run, the capital stock is 9. If the wage rate is $6 and the price p is $18, how much labor does the firm demand? Markets Consider the following cost function: c(q) =16+15q+4q 8. (8 points) Find the firm's individual supply function. 9. (8 points) Find the firm's minimum efficient scale. 10. (8 points) Suppose there are 20 firms with this cost function. What is the market supply function? II. (8 points) What is the long-run supply function of the market?e) (12 points) Graph these curves: a. profit-maximizing labor demand: part d (w on vertical axis, L on horizontal axis) b. short-run supply: part b (P on vertical axis, q on horizontal axis) c. profit: from above (T on vertical axis cal axis, P on horizontal axis) The graphs do not need to be super-accurate but pay attention to the shape of the curves and where they intersect the axes (if they do) () (12 points) Suppose P = P. On the 3 graphs from part e, show what happens when w increases from w, to Wa. Explain how and why labor, supply, and profit change. 2. (54 points) Short-run costs. Suppose w = 1, r = 10 and K = 20. a) (5 points) We have TC = w (#) q' + rk = ()q'+ 200 On one graph (with q on the horizontal axis), graph the Total Cost, Variable Cost, and Fixed Cost functions. Pay attention to the shape of the curves, where they intercept the axes and each other (if they do), and the position of the curves relative to each other. b) (9 points) Using the graph from part a. show how AC, AVC, and MC can be shown when q = 20. c) (5 points) From the TC function in part a, find Marginal Cost, Average Cost, and Average Variable Cost. d) (8 points) Use the function you found in part c. On one graph (with q on the horizontal axis), graph the AC, AVC, and MC functions. Pay attention to the shape of the curves, where they intercept the axes and each other (if they do), and the position of the curves relative to each other. e) (6 points) Calculate the values of AC, AVC, and MC when q = 20. Show these points on the graph from part d. Relative to each other, are the values for AC, AVC, and MC at q = 20 consistent with the results in part b? () (6 points) Calculate the price at which this firm would break even (zero profit). What is the optimal output at this price? 9) (15 points) Suppose the market price is P = 20, What is the firm's optimal output and profit? With respect to profitability, what is the firm's optimal course of action? Explain,Problems 1. Which assumption about consumer preferences does by three different consumers (Augin, Barbara, and each of the following individuals violate? Camina), holding everything else constant Ajam likes basketball more than football; football more than baschall; and baseball more than basketball B. Christina prefers prune juice to orange juice but cannot decide how the fools about grapefruit juice Blake likes superhero comic books but prefers 5 comic books to 10 comic books. 2. By assumption, individual preferences must be tran- sitive so that if A is preferred to B, and B is preferred to C. then A is preferred to C. Suppose that Marsha, 174 24 Jan, and Cindy individually have transitive prefer ences over three goods oranges, apples, and pears. Compute the marginal utility of X for each of the If Marsha, Jan, and Cindy were to vote on whether three consumer at each level of X. to name oranges, apples, or pears the "fruit of the Based on the data in the table, can you tell month." show that it is possible the preferences for whether any of these consumers ire violating any the proup might not be transitive. of the standard assumptions about preferences? 3. Draw two indifference curves for each of the follow- Is it possible that any of these three consumer ing pairs of goods. Put the quantity of the first good have the same preferences, and that columns for the on the horizontal axis and the quantity of the second face consumers differ only because of the arbitrary good on the vertical axis. units that and used to measure utility? Explain Paul likes pencils and pens, but does not care "6. A consumer's utility function is given by Um Xr. which he writes with. Where AfU - Y and MUT=X b. Rhonda likes carrots and dislikes broccoli. What is the utility derived from I unit of X and Emily likes hip-hop iTunes downloads and 2 units of 17 What is the utility derived from docan't care about heavy metal downloads. 2 units of X and I unit of 17 What is the utility Michael only likes dress shirts and cufflinks in 1 derived from $ units of X and 2 units of Y? 10 2 proportions How does the consumer rank the following . Carlene likes pizza and shoes. bundles? "4. Suppose that John is ind ferent between consuming Burdit Quantity of I Quantity of bundle A. which consists of 4 apples and I peach. and bundle I, which consists of 4 peaches and 2 1 apple. If John were given the choice between bun- 10 ile A and bundle C, which contained 3 peaches and 2 apples, which should be pick? (Hint Draw an 1 indifference curve or two,) a 3. The following table displays the total utility (NX ) that corresponds to the number of units of &' consumed
