1. There are 300 identical firms in a perfectly competitive market, the price of the outpu p, the short-run cost function of a typical firm in the market is as follows: C(q) = q³-2q²+2q+10 e. If p = 17, what is this firm's producer surplus? f. What is the short-run market supply function? g. If the market demand function is D = 500 – 50/3p – 2, what is the short-run market equilibrium price and market equilibrium output quantity? h. What is the output level and the profit of a typical firm at the market equilibrium from (g)?
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- A firm in a perfectly competitive industry has patented a newprocess for making widgets. The new process lowers the firm’saverage cost, meaning that this firm alone (although still aprice taker) can earn real economic profits in the long run. a. If the market price is $20 per widget and the firm’s marginalcost is given by MC=0.4q , where q is the dailywidget production for the firm, how many widgets willthe firm produce? b. Suppose a government study has found that the firm’snew process is polluting the air and estimates the socialmarginal cost of widget production by this firm to be. If the market price is still $20, what is thesocially optimal level of production for the firm? Whatshould be the rate of a government-imposed excise tax tobring about this optimal level of production? c. Graph your results.A firm operates in a perfectly competitive market. The market price of its product is 4 birr and the total cost function is given by TC= 1/3 Q3 - 5Q2+20Q + 50, where TC is the total cost and Q is the level of output.a) What level of output should the firm produce to maximize its profit?b) Determine the level of profit at equilibrium.c) What minimum price is required by the firm to stay in the market?Consider a competitive firm with a short-run cost function C(q)=100q-q^2+(1/5)q^3+450(a) Suppose that the market price is $205. Find the optimal output. Find the profitor loss at the optimal output. Will the firm stay or shutdown? Why?(b) Suppose that the market price is $105. Find the optimal output. Find the profitor loss at the optimal output. Will the firm stay or shutdown? Why?(c) Suppose that the market price is $205 and there is a tax of $65 per unit produced. Find the optimal output. Find the profit or loss at the optimal output. Will the firm stay or shutdown? Why?
- 2. Consider a market with 90 firms, each firm has a short-run total cost function as follows: TC(q) = 5q2, and a marginal cost function: MC(q) = 10q. Market demand is given by equation Qd(p) = 200 - p. a) What is the fixed cost? Solve the average variable cost function in the short-run. b) What is the supply function of each firm? c) Solve for the short-run equilibrium outcome: P*, Q* and q*. d) What is one firm's economic profit in this market?2. Consider a market with 90 firms, each firm has a short-run total cost function as follows: TC(q) = 5q2, and a marginal cost function: MC(q) = 10q. Market demand is given by equation Qd(p) = 200 - p. a. What is the fixed cost? Solve the average variable cost function in the short-run. b. What is the supply function of each firm? c. Solve for the short-run equilibrium outcome: P*, Q* and q*. d. What is one firm's economic profit in this market? e. Consider a different market structure, where there is only one firm, interpreted as a monopolist, and then critically discuss the impact on equilibrium price and quantity. Discuss total surplus for these two types of market structures.Can you help with parts d,e and f please? A perfectly competitive firm has the following total cost function: TC = 4,500 + 2q + .0005q2 where TC is total cost in dollars and q is the quantity of output produced. a. Assume this perfectly competitive market consists of 800 firms with cost structures identical to the one above. What is the equation for the market supply curve? Assume the market demand curve is: Qd = 5,600,000 – 400,000P where Qd is the quantity demanded in the market and P is the commodity’s price in dollars. b. What is the market’s equilibrium price? c. Assuming the market is in equilibrium, using marginal revenue and marginal cost determine the firm’s profit-maximizing quantity of output? What does the profit-maximizing firm’s total economic profit equal? Assume the total cost function above: TC = 4,500 + 2q + .0005q2 is associated with the short-run total cost function that corresponds to the minimum point on the long-run average total cost curve and this is a…
- Consider a perfectly competitive market, where the current number of firms is 50. Each firm has one unit of capital and can product q(1, L) = √L units of output with one unit of capital at a cost v per unit, and L units of labor at a cost w per unit in the short-run. a) Find a firm's short-run supply curve, qs(p), and the industry short-run supply curve, Qs(p). b) Given the market demand, = 10000 - 50p, and the industry short-run supply curve, find the short-run equilibrium price and quantity assuming that w = 1.Suppose that the firm operates in a perfectly competitive market. The market price of his product is $4. The firm estimates its cost of production with the following cost function: TC=50+20q-5q2+0.33q3 a. What level of output should the firm produce to maximize its profit? b. Determine the level of profit at equilibrium. c. What minimum price is required by the firm to stay in the market?17.A perfectly competitive firm has the following total cost function: TC = 4,500 + 2q + .0005q2 where TC is total cost in dollars and q is the quantity of output produced. a. Assume this perfectly competitive market consists of 800 firms with cost structures identical to the one above. What is the equation for the market supply curve? Assume the market demand curve is: Qd = 5,600,000 – 400,000P where Qd is the quantity demanded in the market and P is the commodity’s price in dollars. b. What is the market’s equilibrium price? c. Assuming the market is in equilibrium, using marginal revenue and marginal cost determine the firm’s profit-maximizing quantity of output? What does the profit-maximizing firm’s total economic profit equal? Assume the total cost function above: TC = 4,500 + 2q + .0005q2 is associated with the short-run total cost function that corresponds to the minimum point on the long-run average total cost curve and this is a constant cost industry. d. What would the…
- Suppose that many small firms operating in the perfectly competitive market set-up. All firms are identical and have the total cost function c (q)= 40+8q+(q^2/10), where q is the individual firm’s production amount. The market inverse demand function is described as P= A - (Q/50), where A>0 is constant, and Q is the market quantity. In the short-run equilibrium, there are 78 firms in the market, and firm’s maximum profit is $22.5 a) find the short-run equilibrium price b) suppose that in the long-run, firms cost function is still the same C (q)= 40+8q+(q^2/10) (assume LR cost function has fixed component of 40) Find the long-run equilibrium number of firms? (Assume market demand in LR = market demand SR)Suppose a perfectly competitive market has 50 firms, each with supply curve P=50+100Q. The market demand curve is given by P=650-4Q. How much is the individual firm's producer surplus in the short run? a. 400, b. 250, c. 200, d.100Consider a competitive firm with a short-run cost function C(q) = 100q−q2 + 1/5q3 +450. (a) Suppose that the market price is $205. Find the optimal output. Find the profit or loss at the optimal output. Will the firm stay or shutdown? Why? (b) Suppose that the market price is $105. Find the optimal output. Find the profit or loss at the optimal output. Will the firm stay or shutdown? Why? (c) Suppose that the market price is $205 and there is a tax of $65 per unit produced. Find the optimal output. Find the profit or loss at the optimal output. Will the firm stay or shutdown? Why?