__macro homework.

Let us assume a linear technology (that is, a production function with a xed technical coefcient}, according to which output is proportional to the employment level Y = AN, (22) where A is a xed parameter denoting the average productivity of labor [that is, A = Y/ N ) Using equation (22), equation (21) may rewritten as W A ?= (1+a)(1+a)' (211} The unemployment rate that equates {19) with P = P\": and (21') is the 'natural rate of unemployment' (on) It can be obtained by solving the equation 1 F : _ 23 (m'z) (1+#l(1+o') ( ) The solution for an can be oxprcnscd in implict form as an 2 U{,u, 0,2). (24} (+:+1+) Hem the natural rate of unemployment, We obtain, after using the un- employment rate denition and the production function, the 'natural' level of output (Ya), which is given by the expression v, = (1 soars. (25} This is the aggregate supply curve in the medium-run. We call it ASMR. This curve is vertical in the (YP) diagram, being independent of the price level. By employing (24), (25) can be written as K, = Y(,u,,0',z, ALF). (26} (_:_1_] (+} 278 COST CURVES (Ch. 22) (b) The marginal cost function is (c) The level of output that yields the minimum average cost of production is (d) The average variable cost function is. (e) At what level of output does average variable cost equal marginal cost? 22.9 (0) A competitive firm has a production function of the form Y = 24 + 5K. If w = $2 and r = $3, what will be the minimum cost of producing 10 units of output?_NAME 275 car smasher that costs $200 a year to own and then spending $1 for every car smashed into oblivion; the second method involves purchasing a shovel that will last one year and costs $10 and paying the last Carr brother, Scoop, to bury the cars at a cost of $5 each. (a) Write down the total cost functions for the two methods, where y is output per year: TC1 (y) = , TC2(y) = (b) The first method has an average cost function and a marginal cost function For the second method these costs are and. (c) If Rex wrecks 40 cars per year, which method should he use? If Rex wrecks 50 cars per year, which method should he use? What is the smallest number of cars per year for which it would pay him to buy the hydraulic smasher? 22.4 (0) Mary Magnolia wants to open a flower shop, the Petal Pusher, in a new mall. She has her choice of three different floor sizes, 200 square feet, 500 square feet, or 1,000 square feet. The monthly rent will be $1 a square foot. Mary estimates that if she has F square feet of floor space and sells y bouquets a month, her variable costs will be co(y) = y? / F per month. te down her marginal costNAME 275 car smasher that costs $200 a year to own and then spending $1 for every car smashed into oblivion; the second method involves purchasing a shovel that will last one year and costs $10 and paying the last Carr brother, Scoop, to bury the cars at a cost of $5 each. (a) Write down the total cost functions for the two methods, where y is output per year: TC1 (y) = , TC2(y) = (b) The first method has an average cost function and a marginal cost function For the second method these costs are and. (c) If Rex wrecks 40 cars per year, which method should he use? If Rex wrecks 50 cars per year, which method should he use? What is the smallest number of cars per year for which it would pay him to buy the hydraulic smasher? 22.4 (0) Mary Magnolia wants to open a flower shop, the Petal Pusher, in a new mall. She has her choice of three different floor sizes, 200 square feet, 500 square feet, or 1,000 square feet. The monthly rent will be $1 a square foot. Mary estimates that if she has F square feet of floor space and sells y bouquets a month, her variable costs will be co(y) = y? / F per month. te down her marginal costjukes are certainly allowable.) hours of (b) This would cost dollars. (c) Given our production function, the cheapest proportions in which to use jokes and labor are the same no matter how many comic books we print. But when we double the amount of both inputs, the number of comic books produced is multiplied by 22.8 (0) Consider the cost function c(y) = 4y2 + 16. (a) The average cost function is.jukes are certainly allowable.) hours of (b) This would cost dollars. (c) Given our production function, the cheapest proportions in which to use jokes and labor are the same no matter how many comic books we print. But when we double the amount of both inputs, the number of comic books produced is multiplied by 22.8 (0) Consider the cost function c(y) = 4y2 + 16. (a) The average cost function is.274 COST CURVES Ch. 221 AC,MC 30 20 10 10 20 30 40 Output (d) Suppose Otto has to pay $b a year to produce obnoxious television commercials. Otto's total cost curve is now TO(y) = his average cost curve is now AC(?) = . and his marginal cost curve is MC(y) = fe) If 6 = $100, use red ink to draw Otto's average cost curve on the graph above. 22.2 (0) Otto's brother, Dent Carr, is in the auto repair business. Dent recently had little else to do and decided to calculate his cost conditions. He found that the total cost of repairing s cars is TC(s) = 2s' + 10. But Dent's attention was diverted to other things . .. and that's where you come in. Please complete the following: Dent's Total Variable Costs: Total Fixed Costs:. Average Variable Costs: Average Fixed Costs: Average Total Costs: Marginal Costs: 22.3 (0) A third brother, Rex Carr, owns a junk yard. Rex can use one of tro methods to destroy cars. The first involves purchasing a hydraulic