1. A firm uses a single input to produce a commodity according to its short-run production function f(x) = 4\/x, where x is the number of units of input. The commodity sells for $100 per unit. The input cost $50 per unit. (a) the amount of input. (b) Write down a function that states the firm's profit as a function of What is the profit maximizing amount of input and output? (c) its input is subsidized by $10, explain in detail how this will affect the new input Suppose the firm is taxed $20 per unit of its output and the price of and output levels?
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- A firm in a perfectly competitive industry has fixed costs of FC = 15, marginal costs of MC = 5 + 14q, and average variable costs of AVC = 5 + 7q. (a) What are the firm’s variable costs (VC)? (b) What is the firm’s total cost function? (c) If the price is $75, how much does the firm supply? (d) Does the firm continue to supply this quantity in the short-run? (e) Suppose there exists a standard market demand function from consumers (downward slopping). Please provide a logical discussion about how the market achieves short-run equilibrium.2AAWO AC I4 17.1 REVENUE, COST, AND PROFIT APPLICATIONSITSO RSYHAHD 797 20 A firm sells each unit of a product for $50. The total cost of producing x (thousand) units is described by the function C(x) = 10 – 2.5x² + x³ where C(x) is measured in thousands of dollars. (a) Use the marginal approach to determine the profit-maximizing level of output. (6) What is total revenue at this level of output? Total cost? Total profit? 1 The profit function for a firm is -0001. The cost function for a commodity is given by C(x) - 200+12x+0.1x² (S) and the demand funct is p-300-0.02x ($/unit) where x- quantity (demanded and produced). (a) What is the profit function for this commodity? (b) Find the marginal profit function. (c) What is the marginal profit when x-10?! (d) What does this marginal profit tell you? (e) Find the level of demand at which profit is a maximum. Show how you do this using calculus. (1) What is the maximum profit, and what is the selling price that realizes this profit? Ans: R(x)-300x-0.02x², P(x)=-0.12x² +288x-200, P'(10) - 285.6 (S), approximate increase in profit from selling one more unit when sales are at 10 units, solving P'(x)-0 gives max at unit. x-1200 units, max profit - $172,600, price = 300-0.02(1200)-$276 per
- What is the marginal cost associated with producing three units of the contral variable, O (identify point E in the tablej? 36 Total Total Costs Benefits Benefit Net Marginal Marginal Narginal Net Bеnefit Control variable Benefits Cost MB(0) MC (Q) MND (0) Sepped B(Q) C(0) 900 100 800 900 100 800 2 1,700 300 800 200 600 2,400 600 1,800 700 E 400 4 1,000 2,000 600 400 200 3,500 1,500 2,000 500 500 600 1,800 1,400 3,900 2,100 D -200 4,200 4,400 2,800 300 700 -400 200 100 800 800 -600 4,500 4,500 900 -800 10 4,500 5,500 -1,000 1,000 -1,000 Mutiple Choice 50 100 200 300is generally determined by the consumer rather than by the producer. In other words, if a customer perceives that he receives more in benefits than what he has to pay for those benefits (or, he gets more in benefits than what he perceives it costs him to acquire those benefits), then he is probably going to be fairly happy with that product in relation to itsS cost.The graph shows the cost curves are they profit maximizing firm in a competitive market. If the market price is $30 and the firm produces at the profit maximizing quantity, what is the total variable cost A: $5400 B: $7200 C: $3960 D:
- Problem 1 Your firm has determined they use the following production function: q = E°K Assume the current wage rate (w) is $400, the rental rate of capital (r) is $100, and your selling price is $10. (a) If capital is fixed at 5 units, what is your optimal number of employees? (b) What is your profit at this production level? (c) Now, assume you are in the long-run and have signed a contract to produce 250,000 units. How much capital and labor will you use now? Round to the nearest whole number. (d) What is your profit at this production level?What is the marginal benefit associated with producing sx units of the control variable, O (identify point Din the table)? 35 Total variable Benefits Marginal Marginal Marginal Net Benefit Control Total Net Costs Benefits Benefit Cost Sepped B(Q) C(Q) N(Q) MB(Q) MC(Q) MNB (Q) 1. 900 100 800 900 100 800 2 1,700 300 800 200 600 3 2,400 600 1,800 700 E 400 4 1,000 2,000 600 400 200 3,500 1,500 2,000 500 500 6. 3,900 2,100 1,800 D 600 -200 4,200 2,800 1,400 300 700 -400 4,400 B 200 800 -600 008 4,500 4,500 100 900 -800 10 4,500 5.500 -1,000 1,000 -1,000 Mutiple Choice 600 400 200 100Assume the cost of making 30 belts $800 the cost of makin 35 belts $900 and the cost equation is linear. The belts are sold for$ 27 each. a)find the marginal cost b)find a linear equation in slope-intercept, form that represent the total Cost of making will c) What is the fixed cost? d) find a profit in slope- intercept that will represent the profit if x belt are made and sold? e) Find the break even point?
- Problem 4. The marginal cost C' for a product as a function of the number of units produced q is shown in the graph below. The fixed costs are $5,000. marginal cost C' ($/unit) 240 200 160 120 80 40 10 20 30 40 50 60 quantity q (units) (a) Suppose you have already paid the fixed costs. Order the following quantities from least to greatest. Explain. (i) The average cost per unit to produce 60 units (in dollars). (ii) 200 (iii) The cost to produce the first unit. (iv) The average cost per unit to produce 20 units (in dollars). (b) Estimate the average cost per unit to produce a total of 40 units, including the fixed costs.If you were a taxi driver, the daily revenue and cost are as the following: Revenue: $250 Variable cost (gas, your labor…): $190 Mortgage payment for car: $70 License Fee: $30 For profit maximization, will you operate your taxi business today? What is the minimum daily revenue to keep the operation in the short run? What is the minimum daily revenue to keep the operation in the long run? Please show calculation formula and/or equation.(a) Calculate this firm’s marginal cost for output level 5. (b) Calculate this firm’s marginal cost for output level 6. (c) What is the average total cost at which, this firm reaches its break even-point? (d) What is the average variable cost at which, this firm reaches its shut-down point?