Question

In: Economics

Consider a perfectly competitive market in which all firms areidentical. The market is in the...

Consider a perfectly competitive market in which all firms are identical. The market is in the long-run equilibrium, the market equilibrium price is P , and each firm produces   q units of good.

The government decides to impose a tax of size T per unit of good.

a)     After the tax is imposed, how would the market equilibrium price and quantity change in the short-run? How does the quantity produced by each firm change in the short-run? Illustrate your answers using a diagram. (2 points)

b)     After the tax is imposed, is each firm earning a positive or a negative profit in the short-run? Illustrate the profit in the diagram you draw in part a). Will firms enter or exit the market in the long-run? (2 points)

c)     After the tax is imposed, how do the market equilibrium price and quantity change in the long-run? How does the quantity produced by each firm change in the long-run? Illustrate your answers using a diagram. (3 points)

Now consider a technological advancement. For simplicity, consider there is no longer tax imposed by the government in the market. After the technological advancement, each firm can produce twice the quantity of output as before with the same quantity of inputs. Assume the prices of inputs do not change.

d)     Illustrate in a diagram the new average total cost curve and the marginal cost curve after the technological advancement. What is the new minimum average total cost? (Hint: the new efficient scale of each firm is 2q ). (2 points)

e)     Assume demand in the output market is elastic (price elasticity of demand >1). After the technological advancement, how does the market equilibrium price change in the short-run? How does it compare to P/2 ? How does the quantity produced by each firm change in the short-run? Is each firm earning a positive or a negative profit in the short-run? Illustrate using a diagram. Will firms enter or exit the market in the long-run? (4 points)                                                            

f)     Still assume demand in the output market is elastic. After the technological advancement, how does the market equilibrium price change in the long-run? Is the long-run market equilibrium quantity larger than, equal to, or smaller than twice the initial long-run market equilibrium quantity? (2 points)

g)     Now assume demand in the output market is inelastic (price elasticity of demand<1), re-do part e) and part f). A diagram is not required. (4 points)

Solutions

Expert Solution

Long run Equilibrium of perfectly Competitive market occurs at Equilibrium Point E, which determines Equilibrium Quantity Q and Equilibrium price P..

Each firm in the market will be a price taker firm and will produce Quantity as per MR /MC rule.

In the long run, the Equilibrium Point for perfectly Competitive firm will occur where-----

LMC= AR=MR=LAC

So, each firm will earn normal Profit in the long run .

See graph-----

a)when govt imposes tax per unit tax, the supply curve shifts leftwards,to S' ,the Equilibrium Point E' , Equilibrium price will increase and Equilibrium Quantity will decrease in the short run.

In case of firm, the firm will increase production due to increase in market price of good in the short run.

b)Each firm will earn positive Economic Profit in the short run .

New firms will enter the market in the long run.

C) After tax Imposition, market Equilibrium price increases and Equilibrium quantity Decreases due to leftward shift of Supply Curve.

Quantity produced by each firm will increase in the long run.

d) Technological advancement will shift the Supply curve rightward ,the new equlibrium Point will determine price p' below the initial price, and Equilibrium Quantity Q' more than initial Quantity.

See graph-----

In case of firm , ATC curve, MC curve will shift downward.

New minimum average cost is OC .It is equal to AR'(=MR').

New efficient scale of each firm is double the initial Quantity ,that is 2q.

e) When market demand is elastic , the consumers are more sensitive to price, so the market price will decrease in the short run

Equilibrium Quantity produced by each firm will increase in the short run .

Profit of each firm will decrease due to fall in price.

f)The market Equilibrium price will again Increase in the long run because due to fall in price ,demand also Increases in the long run ,and likewise the increase in demand again rraises the price equal to initial equilibrium price P.

The long run market Equilibrium Quantity will be larger than twice the initial long run quantity because demand is elastic .

g) Suppose demand is inelastic ( Ed<1), the market price will not much decrease because consumers are insensitive to price change.

The quantity produced by each firm will be smaller than the initial Quantity produced because people will not buy more as compared to Elastic demand case.

In the long run, market Equilibrium quantity will increase less than the increase in point f.

The Equilibrium market price will again rise to initial price because some firms will exit the market in the long run,the supply will adjust as per the demand in the long run..


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