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- Q1.The following is a Cobb-Douglas production function: Q = 1.75K0.6L0.5. What is correct here? * -This production function displays constant returns to scale -This production function displays increasing returns to scale -A one-percent change in L will cause Q to change by one percent -This production function displays decreasing returns to scale Q2. For studying demand relationships for a proposed new product that no one has ever used before, what would be the best method to use? * -consumer surveys, where potential customers hear about the product and are asked their opinions -double log functional form regression model -ordinary least squares regression on historical data -market experiments, where the price is set differently in two marketsAn employer who employs m workers determines that they produce: units of that product daily. Total income (in dollars) is given by: 1) ¿What is the price, per unit, when there are 30 workers? 2) Determine the marginal revenue when there are 30 workers. 3) The product of marginal income corresponds to the rate of change of income with respect to the number of active employees, at a given moment. Determine the product of marginal revenue when m = 30A firm uses a single input to produce a commodity according to itsshort-run production function f(x) = 4√x, where x is the number of units ofinput. The commodity sells for $100 per unit. The input cost $50 per unit.(a) Write down a function that states the firm’s profit as a function ofthe amount of input.(b) What is the profit maximizing amount of input and output?(c) Suppose the firm is taxed $20 per unit of its output and the priceof its input is subsidized by $10, explain in detail how this will affect the newinput and output levels?
- QUESTION 1a. Is it possible to have diminishing returns to a single factor of production and constant returnsto scale at the same time? Discuss.b. Isoquants can be convex, linear, or L-shaped. What does each of these shapes tell you aboutthe nature of the production function? What does each of these shapes tell you about theMRTS?QUESTION 2a. A firm faces the following average revenue (demand) curve:P = 120 − 0.02Qwhere Q is weekly production and P is price, measured in cents per unit. The firm’s costfunction is given by C = 60Q + 25,000. Assume that the firm maximizes profits.i. What is the level of production, price, and total profit per week?ii. If the government decides to levy a tax of 14 cents per unit on this product, what will be thenew level of production, price, and profit?b. The United States currently imports all of its coffee. The annual demand for coffee by U.S.consumers is given by the demand curve Q = 250 – 10P, where Q is quantity (in millions ofpounds) and P is the…To maximize profit, a price taker will expand its output as long as the sale of additional units adds more to revenues (marginal revenues) than to costs (marginal costs). Therefore, the profit-maximizing price taker will produce the output level at which marginal revenue (and price) equals marginal cost. In a price-taker market, if a business produces efficiently (i.e., that is, where marginal revenues = marginal costs), the firm will be able to make at least a normal profit. True of False. ExplainQuestion You are the manager of a firm and you are required to optimize the Cobb Douglas function given the following parameters. The maximum amount of money available is$1600 where the price of K = 12 and the price of L=6. That is PK=12 and PL=6. The function is given as q=K0.4+L0.6. What is the constraint equation? a. none of the above b. 12K - 6L = 1600 c. 12K/6L = 1600 d. 12K+6L=1600
- Suppose that the total revenue function of a firm is defined as TR= (P)(Q) where TR= f(Q). The usual notation applies. 1. Given its total revenue function, solve for the maximum revenue that the firm can earn. How many units of output should the firm sell to earn that amount of revenue? Note: Solve the problem using simple algebra only. Do not differentiate. 2. What are the roots of the total revenue function? Interpret economically.To maximize profit, a price taker will expand its output as long as the sale of additional units adds more to revenues (marginal revenues) than to costs (marginal costs). Therefore, the profit-maximizing price taker will produce the output level at which marginal revenue (and price) equals marginal cost. In a price-taker market, if a business produces efficiently (i.e., that is, where marginal revenues = marginal costs), the firm will be able to make at least a normal profit. True of False. Explain. All firms produce where MR=MC. Price takers produce and price where P=ATC=MC=MR. That is the "normal profit" level. Profits above that level are considered "economic profits." Review economic profits, normal profits, explicit costs, and implicit costs.2.4 Q7 In the theory of the firm, economist consider the total cost to be a function of the output level Q: C=f(Q). (a) According to the definiton of a function, should each cost figure be associated with a unique level of output? (b) should each leyel of output determine a unique cost figure?
- 1. Imagine that there is an industry for a particular product where the demand for this product is given by P = 100-X. There are two factors of production, capital K and labor L; the price of each will be $1 throughout. The firms all have identical technology, which is given by a fixed coefficients production function: where Y is the level of output and a is some constant from (0, 1). Each firm has fixed costs of 16. (a) Suppose there are precisely six firms in this industry; they can exit if they are unprofitable, but no firms can enter. What is the long-run equilibrium in this case? (Even though there are only six firms, they all entertain competitive conjectures about their effect on various prices.) (b) Suppose there is free entry into this industry. What is the long-run equilibrium? 2. Suppose one firm in a general equilibrium economy has a technology with free disposal Prove that Walrasian equilibrium prices are nonnegative.1 Is it possible for a firm to experience both increasing and diminishing returns at the same time? 2 What other firms, in other industries, might be in similar situations to Microsoft, and in what respects? 3 What is the nature of the fixed factor that is causing the law of diminishing returns in Microsoft’s case? 4 Are there any ways in which Microsoft can reduce the undesirable effects of the law of diminishing returns?COURSE: MICROECONOMICS - PRODUCTION THEORY Suppose a company engaged in manufacture of wheat whose production function is represented by: Q =10KL.In addition, firm must pay wages of $200 and rent on capital is $600. It is known that firm has a budget of $30,000 for cheese production.a) Calculate break-even point of both factors of production and graph itb) What will happen if minimum wage is now fixed at $300? Graph itc) Assuming that new minimum wage at point b) is maintained and, assuming that investor demands a capital rent of $900, explain what happens to optimal factor level. Graph it