Question

9.1. DanielArcher's Midland farm produces com. His cost function (where total cost is measured in cents) is calculated to be + 100g + 1000 c(4) 480 where q is the output level (measured in bushels). The market price of com is 220 cents per bushel which Midland farm, as a competitive pro- ducer, takes as given. How many bushels will Daniel produce? What is Midland farm's shutdown price? 9.2. In Takeout Town, there are 45 identical pizza delivery firms, each firm having the cost function c(g) = 0.5q7 + 4q + 162 where q is the quantity of pizzas produced by a typical firm. The market demand curve is given by Q(p) = 820 – 5p. (a) Find a firm's individual supply curve g(p) and the market sup- ply curve Q(p). Calculate the market equilibrium price p' and quantity Q". Calculate the firm output q and profit level. (b) What will be the long-run price pr after entry or exit? Calculate the approximate number of firms in the long run (round down to the nearest integer). 9.3. In the market for a product, there are 100 identical competitive firms, each firm having the cost function c(q) = 50 + 59 +0.5g? where q is the quantity of output in tons produaæd by each firm. The market demand curve is given by g = 1660 – 20p. (a) Find the market equilibrium price p" and quantity produced by each firm, q". (b) A permanent increase in demand shifts the market demand to Qi = 1920 – 20p. What will be the approximate price p" (up to two decimal places) in this market in the short run? (c) Given the permanent increase in demand, how many firms will there be in this market in the long run after entry or exit? 9.4. In the market for manhole covers, there are 120 identical firms, each firm having the cost function c(g) = 0.5q + 4g + 18 where q is the Competitive Firms 157 number of manhole covers produced by each firm. The market de- mand curve is given by Qd (p) = 1720 – 100p. (a) Find a firm's individual supply curve q(p) and the market sup- ply curve Q(p). Calculate the market equilibrium price p* and quantity Q'. Calculate the output q* thateach firm produces and a typical firm's profit level. (b) The government imposes a tax of $1 per manhole cover produced on each firm. What will be the long-run price pi, after entry or exit? If the tax remains in place, calculate the approximate num- ber of firms in the long run (round down to the nearest integer).

Answer 1

Answer 9.1=

c(q)=q^3/480 -q^2/2+ 100q+1000

Under perfect competition equilibrium occurs where MC=P

MC=dc(q)/dq= q^2/160- q+100

P= 220 cents or $2.2

MC=P

q^2/160-q+100= 220

q^2 -160q-19200=0

q^2+240q-80q-19200= 0

On solving,

q=240 or q=-80

Therefore Daniel will produce 240 bushels.

Shutdown price is at the lowest point of AVC

AVC= c(q)/q= q^2/480- q/2+100

Minimum point of AVC can be found by differentiating AVC with respect to q , then equating it to zero.

dAVC/dq= q/240-1/2=0

q= 120

AVC when q=120 is equal to (120)^2/480 -120/2 +100=30-60+100= 70 cent

Lowest AVC is when q=120, AVC= 70 cent

Shutdown price= 70 cent.

Note-According to HOMEWORKLIB RULES first question is answered.