587 words - 3 pages

A monopoly firm faces a demand curve given by the following equation: P = $500 − 10Q, where Q equals quantity sold per day. Its marginal cost curve is MC = $100 per day. Assume that the firm faces no fixed cost. You may wish to arrive at the answers mathematically, or by using a graph (the graph is not required to be presented), either way, please provide a brief description of how you arrived at your results.

a) How much will the firm produce? b) How much will it charge? c) Can you determine its profit per day? (Hint: you can; state how much it is.) d) Suppose a tax of $1,000 per day is imposed on the firm. How will this affect its price? e) How would the $1,000 per day tax its output per day? f) How would the $1,000 ...view middle of the document...

Therefore MR = 500+ 2x -10Q iii) the firm will produce where MR = MC = 500-20Q=100 solving for Q we get 20b) How much will it charge? The demand equation is P=500-10QSubstituting Q in the equation we get P=500-(10x20) = 300c) Can you determine its profit per day? (Hint: you can; state how much it is.) Marginal cost is constant hence MC=AVC.MC=100=TC=MC x Q = 100x20=2000Profits = TR-TC TR= PQ= 300 x 20 = $6000 Profit = 6000-2000=$4000d) Suppose a tax of $1,000 per day is imposed on the firm. How will this affect its price? i) Increase in tax reduces the output and raises the price. ii) P = $500 − 10Qiii) From (e) below, quantity is 15iv) Therefore, P=500-(10x15) = $350e) How would the $1,000 per day tax its output per day? Tax of $1000 reduces profit to $3000 from $4000If Q of 20 produces profit of $4000, then $3000 will be produced by; (20x3000)/4000 =15.Therefore, output reduces to 15f) How would the $1,000 per day tax affect its profit per day? P=TR-TCP= (15 x 350) - (100x15) = 5250-1500 = $3750Reduction in profit is $(4,000-3750) = $250g) Now suppose a tax of $100 per unit is imposed. How will this affect the firm’s price? i) Tax of $100 reduces profit to $(4000-100) =$3900ii) If quantity 20 produces profit of $4000, then $3900 is produced by (3900x20)/4000 = 19.5...

Profit maximizing firm will produce where mc =mr 2 a monopoly faces a mr curve with the twice the slope of the demand curve hence mr = 500+ 2x -10Q 3 therefore they will produce where mr = mc = 500-20Q=100 solve for Q . we get 20 4 to find the price plug Q=20 to the Demand equation P = 500 -10 x 20 = 300 5 Mc is constant therefore MC=avc therefore 100x 20 = tc = 2000 6 profits tr-tc tr= 300 x 20 = 6000 6000-2000=4000

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