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Econ 302 Homework #3 Assignment




Question;Instructions: Please Read CarefullyPlease print out this form. There should be four separate sheets of paper (including the coversheet). After you have written your answers, please staple the four sheets together at the top lefthand corner.The first sheet is intended only as a cover sheet. Do not write anything on the first sheet except yourname and ID #.Please answer each question on the page provided. If you need extra space, you may use the backof the sheet.There are 50 possible points on this homework assignment. You may work together, but youMUST WRITE UP YOUR OWN WORK and TURN IT IN, IN PERSON, AT THE BEGINNINGOF CLASS on Friday, March 22nd. Late homework will not be accepted.PLEASE STAPLE YOURHOMEWORK!!1. (20 points) Suppose honey is produced in a beehive using bees and sugar. Each honey producer usesone beehive which she rents for $20/month. Producing q gallons of honey in one month requiresspending 5q dollars bees, and 4q2 dollars on sugar.a) (5 points) What is the total cost of producing q units of honey for an individual honey producer in agiven month?b) (5 points) In general, if the total cost of producing honey is a + bq + cq 2, then the marginal cost ofproducing honey is b + 2cq. Assuming each honey producer operates as a price-taker, what is themonthly supply curve for an individual producer?c) (5 points) Let Q be the total market supply, and q is the supply of an individual firm. Therefore, q =Q/n where n is the total number of firms in the market. Suppose the demand for honey is given by Q =512-4P. Also, suppose there are 50 honey producers in the market. What is the equilibrium price ofhoney?d) (5 points) How much profit does an individual producer make in a month? Is this a long-runequilibrium? If the answer is yes, simply state that it is a long-run equilibrium. If the answer is no,explain whether or not the equilibrium price will rise or fall.2. (21 total points) Suppose a firms production function is given by Q = L 1/2*K1/2. This means thatMPL =K 1/ 2L1 / 2, and MPK =.2 L1 / 22K 1/ 2Suppose the price of labor is w = 36, and the price of capital is r = 64.a) (9 points) Derive the firms Total Cost function, TC(Q). Be sure to show your work!b) (12 points) For this problem, you will sketch the graph of the firms isoquant for Q = 12 units ofoutput, and on the same graph sketch the firms isocost line associated with the total cost of producing Q= 12 units of output. To get this total cost, you must use the Total Cost function from part a). Pleasescale your graph up to 36 units of Labor on the horizontal axis, and 36 units of Capital on the vertical axis(do not go above 36 units on either axis). For the isocost line, clearly identify the vertical and horizontalintercepts. For the isoquant, clearly identify 4 combinations of Labor and Capital that will produce Q =12 (including the bundle that minimizes the firms cost of production). Make sure your graph is neatlyand accurately drawn and carefully labeled.3) (9 total points) Suppose there are n identical firms in a market. Each firm has fixed cost equal to 392,and variable cost given by VC = 2q2, where q is the amount that an individual firm produces. This meansthat an individual firms marginal cost is given by MC = 4q. Also, the market demand is given byP = 1148 3Q, where Q is the total amount of the good produced by all of the firms combined.Therefore, Q = n*q.a) How much output will each of them produce?b) What will be the market price?c) How many firms will there be in long run equilibrium?


Paper#55938 | Written in 18-Jul-2015

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