The demand equation for handcrafted violins by a certain violin maker can be approximated by p=20-x where p is the price in thousands of dollars and x is the quantity of violins demanded. Find and interpret the marginal revenue for each of the given production levels. (a) x = 7 (b) x = 10 (c) x = 11
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- A Los Angeles firm uses a single input to produce a recreational commodity according to a production function f(x)=4x1/2, where x is the number of units of input. The price of the commodity is $100 per unit, and the input cost is $50 per unit. The fixed costs are zero. A: Write down the firm’s profit function. C:Find the profit maximizing amounts of input and output. What is the maximum profit? C:Suppose that the firm is taxed at $20 per unit of its output (note it is a quantity tax) and the price of its input is subsidized by $10 per unit. What is the new input and output levels? What is the new maximal profit?A 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?The marginal and average total cost curves for barbers in an area are cosntant at $12.00/haircut. The daily demand curve for haircuts in the area is given by: P = 22 - 0.001Qd where P is the price in dollars per haircut and Qd is the daily quantity demanded in number of haircuts. Haircuts are provided in a perfectly competitive market and each barber can provide exactly 25 haircuts daily. Suppose that the government decides to limit the number of barbers to 320. Each year, barbers must obtain a government-issued license to cut hair. Based upon the previous information: a. What will be the long-run equilibrium price for a haircut given there are only 320 licensed barbers?b. How much economic profit will each licensed barber earn daily?
- A firm uses a production function of the form Y=z*K^0.33*Nd^0.67 and chooses labor input Nd to maximize profits taking the wage rate w that it pays per unit of labor as given. First, write down the profit function of the firm. Assume z=10, K=100, and wage w = $20. The government now introduces a wage subsidy to help out the firm. The wage subsidy s = $4 per unit of work. Given this subsidy solve for the new optimal output level of the firm. Y* =A firm’s profit is given by the following function, which maps output q ≥ 0 onto profit (revenue minus cost). π(q) = 11q − (q 2 + 2q + 10) = −q 2 + 9q − 10, The firm is constrained by a quota such that output q cannot be greater than a value Q. (a) What is the domain of this profit function? 1 of 2 ECON10071/20071 - 2020/21 (b) Given this, what is (global) profit maximising output when (i) Q = 6, and when (ii) Q = 2.Suppose the demand for a product X produced by a company AAA is given by the following function: QX = 2000 - 250*PX. At what price per item of the product X (EUR) can this copmany maximize its total revenues? Fill in the Table gaps: Demand function Price function Total Revenue (EUR) Marginal Revenue (EUR) Quantity Price per product (EUR) Q = 2000 - 250P P = ? TR = Q*P MR = dTR/dQ = 0 Q = ? P = (2000 - Q)/250 250P = 2000 - Q TR = Q*(2000 - Q)/250 MR = 8 - 2*Q/250 Q/125 = 8 P = (2000 - 1000)/250 P = (2000 - Q)/250 TR = 8*Q - Q^2/250 8 - Q/125 = 0 Q = 1000 P = 4 Alternative solution Demand function Total Revenue (EUR) Marginal Revenue (EUR) Price per product (EUR) Q = 2000 - 250P TR = Q*P MR = dTR/dP = 0 2000 - 500*P = 0 TR = (2000 - 250P)*P MR = 2000 - 2*250*P 500*P = 2000 TR = 2000P - 250P^2 MR = 2000 - 500*P P = 4
- Suppose the demand equation is 200x + 10p = 10000, where x is the num- ber of items sold when the per unit price is p dollars. Determine (a) the rev- enue function,(b) the domain of the revenue function,(c) the revenue derived from the sale of the 20th item the marginal revenu(de)wthen x = 20,level of production that maximizes the revenue,and the maximum revenue.Market Failures in Imperfect Competition Efficiency in exchange is satisfied with the equality between MRS and price ratios of the goods. Efficiency in production is satisfied with the equality between MRTS and the price ratios of factor markets (labor and capital; hence, wage and rent). Efficiency in product mix is normally not satisfied under imperfect competition because MRS is not equal to MRT. Answer the following: a. If there is an imperfect competition in both the goods market (X and Y), say that Px/Py is both under monopoly, is it possible for economic efficiency to be reached? How? Explain in words and mathematically. b. If there is an imperfect competition in both the two factor market (L and K), say that w/r or Pl/Pk is both under monopoly, is it possible for economic efficiency to be attained? How? Explain in words and mathematically.Nousaku estimates that the total daily revenue of producing q units of KAGO basket is (R(q) = (102 - (675/q+4) - q) thousand yen. What is the marginal revenue when output is 6? Interpret your answer.
- Windies Cricket manufactures Windies supporter jerseys. The quantity q, of thesejerseys demanded weekly is related to the wholesale price per jersey p, by thefollowing equation:? = −0.006? + 15The weekly total cost incurred by Windies Cricket for producing q jerseys is:?(?) = 38? − 0.02?2 + 30,000a. Determine an expression to represent the weekly Revenue functionb. Determine an expression to represent the weekly Profit function.c. Calculate the weekly Revenue when ten dozen jerseys are produced and sold.d. Will Windies Cricket record a loss or profit if they were to produce and sell 2450jerseys?e. If Windies Cricket wishes to maintain a total cost less than $42,000.00, whatrange(s) of Windies jerseys should be produced. f. Calculate the equilibrium price and quantity for Windies jerseys.Suppose the revenue (in dollars) from the sale of x units of a product is given by R(x) = 56x2 + 65x 2x + 2 . Find the marginal revenue when 25 units are sold. (Round your answer to the nearest dollar.)$ Interpret your result. When 25 units are sold, the projected revenue from the sale of unit 26 would be $ .a) Calculate the technical rate of subsitution b) Derive the cost function c(w1,w2,y) c) When w1 = 5 and w2 = 8, calculate the average cost AC(y) and the marginal cost MC(y). For y > 0, which one is larger, AC(y) or MC(y)? d) When w1 = 8 and w2 = 9, derive the supply function y(p) e) Suppose that Pot & Gold Inc has to pay a quasi fixed cost of $50. When w1 = 8 and w2 = 9, derive the supply function y(p) for Pot & Gold Inc