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- 8. The production function for a price-taking firm is given by q = 2.5k0.4L0.4. What is the supply function q(v,w,p)? [Show your work]13) You begin to work at a factory that produces Aguardiente (Firewater, a type of alcoholic beverage), the function of production its represented by the technology: Q(L, K, Z) = L³K+zł Where with offers of input perfectly elastic A) Salary w is the price of labor L. B) Interest r is the price of capital K. C) Rent q is the price of drinkable alcohol Z. Calculate The function of demand for each input The function of offer for the Firewater The function of total costs for the Firewater The maximum benefit.1. A firm’s production function is , where Ldenotes the size of the workforce. Find the value of MPLin the case when: (a) L=1, (b) L=10, (c) L=100, (d) L=1000 Does the law of diminishing marginal productivity apply to this particular function? 2. Show that the price elasticity of demand is constant for demand functions of the form where A and n are positive constants. 3. The demand and total cost functions of a good arerespectively and a) Find expressions for TR, (profit) , MR, and MC in terms of Q. b) Solve the equation and hence determine the value of Q which maximizes profit. c) Verify that, at the point of maximum profit, MR=MC. 4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components: (a) GH¢10 million for the land (b) GH¢1/4 million per floor (c) Specialized costs of GH¢10000x per floor. How many floors should the office complex contain if the average cost per floor is to be minimized? 5. The supply…
- 6. Each of the 10 firms has the production function q = √KL. The wage is 5 and the rent on capital is 10. Assume we are in the long run, so firms can vary both factors. Write an expression for one firm's cost minimization problem. Use whichever method you prefer to minimize cost and derive an expression for one firm's total cost: TC (9₁) c. Compute one firm's marginal cost and derive the inverse supply curve for one firm and the inverse supply curve for the market. What is the elasticity of supply? a. b.The following graph plots daily cost curves for a firm operating in the competitive market for demin overalls. Hint: Once you have positioned the rectangle on the graph, select a point to observe its coordinates. PRICE (Dollars per overalls) 50 45 40 35 15 10 5 0 0 2 MC ATC AVC 10 12 4 8 14 16 QUANTITY (Thousands of overallses per day) 18 20 In the short run, given a market price equal to $15 per overalls, the firm should produce a daily quantity of The rectangular area represents a short-run Profit or Loss On the preceding graph, use the blue rectangle (circle symbols) to fill in the area that represents profit or loss of the firm given the market price of $15 and the quantity of production from your previous answer. Note: In the following question, enter a positive number regardless of whether the firm earns a profit or incurs a loss. of $ overallses. thousand per day for the firm.13) You begin to work at a factory that produces Aguardiente (Firewater, a type of alcoholic beverage), the function of production its represented by the technology: Q(L, K, Z) = L³ K+z! Where with offers of input perfectly elastic A) Salary w is the price of labor L. B) Interest r is the price of capital K. C) Rent q is the price of drinkable alcohol Z. Calculate The function of demand for each input The function of offer for the Firewater The function of total costs for the Firewater The maximum benefit.
- 2. The market for a slice of pizza in Oakland is highly competitive. The market demand for a slice of pizza can be summarized by the function: D(p) = 1200 — 200p. Consider each pizza shop to be an individual firm with the 1 same cost function C(q) = FC + - q2, where FC represents fixed cost of renting a space from which to sell pizza, and the variable costs reflect the cost of the labor involved in producing and selling pizza. a. In the short-run (e.g. the six months following the signing of a lease for a space from which to sell pizza) determine the quantity each pizza shop would produce for any price in the market. b. In what way does your answer to part (a) depend on the fixed cost? Explain your answer in no more than two sentences. c. Suppose initially there are 100 pizza shops selling pizza in Oakland. Derive an expression for the short-run market supply for pizza. d. Find the short-run equilibrium price and quantity in the Oakland pizza market. How does this equilibrium depend on…The following graph plots daily cost curves for a firm operating in the competitive market for demin overalls. Hint: Once you have positioned the rectangle on the graph, select a point to observe its coordinates. PRICE (Dollars per overalls) 50 10 10 5 0 MC 2 ATC 8 18 QUANTITY (Thousands of overallises per day) AVC 10 20 Profit or Loss In the short run, given a market price equal to $15 per overalls, the firm should produce a daily quantity of On the preceding graph, use the blue rectangle (circle symbols) to fill in the area that represents profit or loss of the firm given the market price of $15 and the quantity of production from your previous answer. Note: In the following question, enter a positive number regardless of whether the firm earns a profit or incurs a loss. The rectangular area represents a short-run thousand per day for the firm. $ overallses.The following graph plots daily cost curves for a firm operating in the competitive market for instant pots. PRICE (Dollars per instant pot) 100 90 80 70 60 50 40 30 20 10 0 0 D 5 25.00 70.00 Price (Dollars per instant pot) MC 100.00 ATC AVC 10 15 20 25 30 35 40 QUANTITY (Thousands of instant pots) Using the following table, for each price level, calculate the optimal quantity of units for the firm to produce. Using the data from the graph to determine the firm's total variable cost, calculate the profit or loss associated with producing that quantity. Assume that if the firm is indifferent between producing and shutting down, it will choose to produce. (Hint: Select purple points [diamond symbols] on the graph to receive exact average variable cost information.) Quantity (Instant pots) 45 50 Total Revenue Fixed Cost (Dollars) (Dollars) 1,600,000 1,600,000 1,600,000 Variable Cost (Dollars) Profit (Dollars) If the firm shuts down, it must incur its fixed costs (FC) in the short run. In…
- A firm has a linear demand function for its product. When the price of the product isSh.220, the quantity demanded is 40 units. When the price increases to Sh.240, thequantity demanded becomes 30 units. In addition, the firm’s marginal cost function isgiven by:MC = 40q – 2q2 + 2Fixed cost = Sh.5 millionWhere q = quantity demanded, MC = marginal cost (Sh. million)Evaluate the level of output that maximizes profits.2. Firm A makes and sells motor cycles. The total cost of each cycle is the sum of the costs of frames, assembly and engine. The firm produces its own engines according to the cost equation C₁=250,000 + 1,000Q +5Q² The cost of frames and assembly is $2,000 per cycle. Monthly demand for cycles is given by the inverse demand equation: P = 10,000-30Q Calculate the MC of producing an additional engine.4. A puppet maker calculates that the yearly cost of running his manufactory is $14,000. Additionally it costs him $60 to create each of his puppets. The price per puppet is determined by the following price-demand equation: p=500–2x a. Find the Cost equation for the total number of puppets produced and sold Find the Revenue equation for the total number of puppets produced and sold b. c. How many puppets does he need to make and sell to break even? d. Use the Cost and Revenue equations to find the Profit function What is the price that he needs to charge if he wants to sell exactly 80 puppets? e.