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A monopolist is deciding to practice 2nd degree price discrimination according to quantity consumed, i.e. pricing in blocks. Without price discrimination he charges 120 . Price elasticity of demand he faces is equal to −1,5. Marginal cost is MC=Q+20. Fixed costs are 0. (a) What are price, output, and profits if there is no price discrimination. Also define the demand function (assume it is linear) (b) Now monopolist uses 2 nd degree price discrimination. Calculate the size and price for each block if 1 st block is 10 . What the total quantity of blocks? Use the demand function from

(A). Hint: use Stackelberg rule. Also see Гребенников, гл.5
(B) What are the profit and consumer's surplus? Show it on the graph.
(C) Suppose the total quantity of blocks is that of
(D), but the size and price for each block is not defined. What are the optimal size and price for each block. What is profit?

User Johowie
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Final answer:

To determine optimal pricing and output without price discrimination, one must know where MR = MC, which we can't establish without a complete demand function. With 2nd degree price discrimination, block sizes and pricing would vary to maximize profits, but again specific calculations require the demand function. Profits and consumer surplus would be determined as areas under the demand and above the price curves.

Step-by-step explanation:

To solve for price, output, and profits without price discrimination, we start with the given price elasticity of demand (PED) of -1.5 and the monopolist's price (P) of $120. We also know the marginal cost (MC) is given by MC = Q + 20, where Q is the quantity. Since fixed costs are zero, average total cost equals marginal cost.

Firstly, to define the demand function, we would typically need two points to construct a linear equation, but because we only have the elasticity and one price, we're limited in establishing the exact demand function without additional information. However, it is generally stated that to maximize profits, a firm will set its output where marginal revenue (MR) equals MC. Without the complete demand function, we cannot identify the MR curve, but we know that with a price of $120 and an elasticity of -1.5, the firm is operating on the elastic portion of its demand curve, suggesting that it potentially is at its profit-maximizing level because MR is positive. Still, this cannot be concluded with certainty.

Secondly, with 2nd degree price discrimination based on quantity, the monopolist would create blocks of goods and charge a different price for each block. Given that the first block is 10 units, the firm would use the Stackelberg model for pricing subsequent blocks. However, without a defined demand function, we cannot offer an exact solution for block sizes or prices. Typically, the monopolist would set a lower price for each additional block to encourage consumers to purchase more, increasing total quantity sold.

Profit and consumer surplus would be calculated using the areas under the demand curve and above the price for each block. Profit would be the total revenue minus total costs, which incorporates the variable costs represented by MC and any fixed costs, which in this scenario are zero.

Lastly, when determining the optimal size and price for each block, the monopolist would consider the marginal cost of each block as well as how much consumers are willing to pay for additional units. The firm aims to maximize the difference between total revenue and total costs.

User TylerH
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