There are three companies - Ceramic, Pottery and Tile - producing mugs. The production function of mugs for Ceramic is given by Qc = 10K0.5 10.5, where K is hours of machine time and L is hours of labour employed. Pottery's production function of mugs is Qp = 10K0.6 10.4 and Tile's production function of mugs is QT = 20K0.6 10.5 a) Using a graph show how, ceteris paribus, an improvement in technology would affect Ceramic's production function. b) If all companies use the same amount of capital and labour, which will generate more output? Explain. c) Find the marginal product of capital and the marginal product of labour for each company. d) Assume that K = L = 2,000. Which company will benefit the most from increasing its labour? Which company will benefit the most from increasing its capital? Why? e) What type of returns to scale is each company exhibiting? Explain.

Question # 1: Majeda wrote the following answer on her microeconomics examination: “Virtually every production function exhibit diminishing returns to scale because my professor said that all inputs have diminishing marginal productivities. So, when all inputs are doubled, output must be less than double." How would you grade Majeda's answer? Question # 2: Suppose a firm had a production function with linear isoquants, implying that its two inputs were perfect substitutes for each other. What would determine the firm's expansion path in this case? For the opposite case of a fixed-portions production function, what would the firm's expansion path be? Question # 3: Suppose that a firm's production function is q = 30√L. In the short run, where there are fixed costs of $2,200, and labor is the variable input whose cost is $6,300 per units. What is the total cost of producing 20 units of output?

Hannah and Sam run Moretown Makeovers, a home remodeling business. The number of square feet they can remodel in a week is described by the Cobb-Douglas production function             Q=F(L,K)             Q=10L^0.5K^0.5,where L is their number of workers and K is units of capital. The wage rate is $250 per week and a unit of capital costs $250 per week. Suppose that when initially producing 100 square feet a week, they use 10 units of capital.a. What is their short-run cost of remodeling 1,000 square feet per week?    Instructions: Enter your answer as a whole number.    $ b. What is their long-run cost of remodeling 1,000 square feet per week?    Instructions: Enter your answer as a whole number.    $

Question 5: Suppose a brewery uses a Cobb-Douglas production function for his production. He studies the production process and finds the following. An additional machine-hour of fermentation capacity would increase output by 500 bottles per day (i. e. MPK = 500). An additional man-hour of labor would increase output by 1000 bottles per day (i. e. MPL = 1000). The price of a man- hour of labor is $50 per hour. The price of a machine-hour of fermentation capacity is $5 per hour. 1. Is the brewery currently minimizing its cost of production? Check using the minimization condition. 2. It turns out, the brewery is not optimally chossing the factors of production. To lower its production cost, which factor of production should the brewery increase and which factor should he decrease? 3. Suppose that the price of a machine-hour of fermentation capacity rises to $25 per hour. How does this change the answer from part 1?

Kwami and Adzga quit their jobs and decided to start a piggery joint venture business. The company processes and packs pork for sale. The output from this firm is described by the Cobb-Douglas production function, q=K¹/² A¹/2 Where q is the number of pigs processed in a quarter, K is the number of hours invested by Kwami in a quarter, and A is the number of hours invested by Adzoa in a quarter. Kwami and Adzoa value 1 hour of their time at $12 and $3 respectively based on what each was earning before quitting their jobs. a) Obtain the number of hours that Adzoa needs to invest (as a function of q and K) for 150 pigs to be processed in a quarter b) How many hours should Adzoa invest for 150 pigs to be processed in a quarter if it is known that Kwami invested 750 hours? c) The cost function for this company may be written as, C= vK + WA where v and w are unit costs for Kwami and Adzoa. wwwwwwww www Substituting for v and w gives C= 12K + 3A Express this cost of production function as a…

A small clothing manufacturer employs a production method that is approximated by the following production function: q=12KL², where L measures the number of labor hours and K measures the number of rental hours for the machines used in the clothing construction process. Does this production process exhibit increasing, decreasing, or constant returns to scale? Briefly explain your answer. The hourly wage rate for workers at this company is $15; and the rental cost on the machines is $75 per hour. The company has a total budget of $3,150 that it can allocate to cover weekly production costs. The goal of the company's owner is to maximize their output, subject to the constraint of their production budget. Determine the output-maximizing levels of labor and capital the owner will employ.

Suppose that the profit from the sale of Kisses and Kreams is given by the following, where x is the number of pounds of Kisses and y is the number of pounds of Kreams. P(x, y) = 10x + 6.6y - 0.001x² -0.025y² dollars You know from previous experience that, for such a profit function, profit will be maximized at the critical point of P(x,y). (a) Determine the amounts of Kisses and Kreams that will maximize profit. pounds of Kisses pounds of Kreams (b) What is the maximum profit? (Round your answer to two decimal places.) $

Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started looking at the cost function C (æ), the cost of a firm producing z items. An important microeconomics concept is the marginal cost, defined in (non- mathematical introductory) economics as the cost of producing one additional item. If the current production level is æ items with cost C (z), then the cost of computing h additionial (C(z+h)-C(z)) items is C (z + h). The average cost of those h items is . As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h → 0, i.e. the derivative C' (z). Use this function in the model below for the Marginal Cost function MC (x). Problem Set question: The cost, in dollars, of producing z units of a certain item is given by C (z) = 0.02a3 – 10z + 450. (a) Find the marginal cost function. MC (z) (b) Find the marginal cost when 50 units of the item are produced. The marginal cost when 50…

Suppose the production function is given by G = 10K - 8L. What is the average product of capital when 2 units of capital and 10 units of labor are employed?

Find out the maximum possible output for a firm with two units of L and 50 units of k when its production function is Q = 5L + 3K