Please help with a couple questions... (explantions would be greatly appreciated

Question

Please help with a couple questions... (explantions would be greatly appreciated)

Suppose we have 100 people enter a lottery. Each of individual has initial wealth of $50,000. The price of a lottery is $10. The prize of the lottery is given as the number of people entering the lottery times the price of a lottery. Out of 100, 5 people will be selected as the winner, and the prize money will be divided equally among them. Decide whether it is a favorable gamble or not and give the reason why. Kiwi Inc. dominates the wholesale chicken market in New Zealand. Its production cost is: long-run average cost LAC = long-run marginal cost LMC = $2 per pound and demand is given by P = 6-2Q, where P denotes price per pound and Q denotes output (in millions of pounds). Determine Kiwi's output and price (presuming it faces no other competitors). Suppose Kiwi Inc. conducted a market survey and found that the New Zealand wholesale market for chicken can be divided into two segments with the demand functions given by P1 = 12-Q1 and P2= 3-3Q2. If Kiwi Inc. are able to discriminate the price between these two market segments and resale is impossible between the two segments, what price should Kiwi Inc. charge for each market segment? Compare the profit for Kiwi Inc. in part (a) and (b). Which profit is higher?

Explanation / Answer

2.

a.

Output and price could be calculated as below:

Price (P) = 6 – 2Q

TR = (6 – 2Q) × Q = 6Q – 2Q^2

MR = 6 – 4Q

MR = MC

6 – 4Q = $2

Quantity, Q = 1

Price (P) is (6 – 2×1 =) $3

b.

Given, P1 + P2 = P

Price (P1) = 12 – 6Q1

TR = (12 – 6Q1) × Q1 = 12Q1 – 6Q1^2

MR = 12 – 12Q1

MR = MC

12 – 12Q1 = $2

Quantity, Q1 = 10/12

Price (P1) is {12 – 6×(10/12) =} $7

Price (P2) = 3 – 3Q2

TR = (3 – 3Q2) × Q2 = 3Q2 – 3Q2^2

MR = 3 – 6Q2

MR = MC

3 – 6Q2 = $2

Quantity, Q2 = 1/6

Price (P2) is {3 – 3×(1/6) =} $2.5

c.

Profit of quantity = 1 and price = $3:

Profit of ‘a’ = TR – TC = ($3 × 1) – ($2 × 1) = $1

Profit of quantity = 10/12 and price = $7:

Profit = TR – TC = {(10/12) × $7) – ($2 × 10/12) = $50/12

Profit of quantity = 1/6 and price = $2.5:

Profit = TR – TC = {(1/6) × $2.5) – ($2 × 1/6) = $0.5/6

Total profit of ‘b’ = $50/12 + $0.5/6 = $4.25

Answer: a’s profit is $1 and b’s profit is $4.25. Therefore, b’s profit is higher than a.

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