Based on Figure 1 which summarizes the demand marginal reven

Based on Figure [1] (which summarizes the demand, marginal revenue, and relevant costs for your product), determine your firm\'s optimal price, output, and the resulting profits for each of the following scenarios: You charge the same unit price to all consumers. You engage in first-degree price discrimination. You engage in two-part pricing. You engage in block pricing.

Solution

a. When producer choose fixed price then, two cases can be happen:

for perfectly competitive market equilibrium is at P=MC

Now, P=PQ/Q=TR/Q=AR=Demand curve

Here P=$40 and corresponding to P=MC we have 30units of output. In perfectly competitve market profit is zero.

On the otherhand, if the firm is monopoly then equilibrium is at MR=MC

Here P=$100 and corresponding to MR=MC it produces 15units of output.

Here, total revenue(TR)=PQ=$100x15=$1500 and total cost(TC)=$40x15=$600

Hence, profit=TR-TC=$900

b. First degree price discrimination is a form of price discrimination in the monopoly market where producer appropriates the entire consumer surplus. Consumer surplus is the difference between the consumer\'s willingness to pay and he ends up actually paying for that good. It is the area under the demand curve and over and above the expenditure area. If producer produces monopoly output then, price is $100, output is 15units, profit is $900 and producers surplus is $[1/2x(160-100)x(15-0)]=$30x15=$450, corresponding to that profit=$60x15=$900. Again if it focus upon sales maximization then, it produces upto competitive output with price level $40, output=30units and producers surplus=$[1/2x(160-40)x(30-0)]=$120x30=$3600 and profit is 0.

c. Two part tariff is charging double price. It is charging lower to a group of consumer who wants to have a lower expenditure and higher to those who is ready to consume more. For example, we may say, producer can fix a minimum rate to enter an amusement park but for rides it charges higher. How much higher depends on the mark up pricing, P=MC/(1-1/e)

For the entrants minimum price and output is $40 and 30units. Now if it charge two part tariff it will produce as much as 15units at price $100

Profit(z) here=2T+(P-MC)(Q1+Q2);T= consumer surplus who give two part tariff

So, z=$[2x450+(100-40)(15+30)]=$(900+60x45)=$(900+2700)=$3600

d. Block pricing is allowed for the second degree price discrimination. In this case producer appropriates the least consumer surplus by charging different price for different units. If that produces upto competitive output then, price is $40, output is 30units and consumer surplus: $1/2[(160-140)(5-0)+(140-120)(10-5)+...+(60-40)(40-35)]=$(1/2x20x5x6)=$300

Hence, profit is $[(140-40)x5+(120-40)x10+(100-40)x15+(80-40)x20+(60-40)x25]

=$(100x5+80x10+60x15+40x20+20x25)=$(500+800+900+800+500)=$3700