OK HERE ARE THE CORRECTIONS. IN PROBLEM 2 THE ANSWER TO #1 IS $2 PER GALLON OF GAS. HE SAID USING THIS YOU COULD SOLVE THE REST OF THE PROBLEMS. I HOPE!!!

PLEASE SEE ATTCHMENT

Problem 1.

Part A: A firm with âmarket powerâ is operating two plants and

selling its product in two markets. The demand and cost configurations

it faces are:

Demand: Costs:

Market 1: P = 484 â 20Q1 Plant 1: TC1 = 961 â 10 Q1 + EQ

QO(sdo4(1),sup4(2))

Market 2: P = 484 â 5Q2 Plant 2: TC2 = 324 â 10 Q2 +3 EQ

QO(sdo4(2),sup4(2))

On the demand side, Q1 represents the amounts sold in market 1 and Q2

represents the amounts sold in market 2. On the cost side. TC1

represents the total cost of producing Q1 level of output in plant 1

and TC2 represents the total cost of producing Q2 level of output in

plant 2.

Given the demand and cost figures above,

1. How much will this firm sell in each of the two markets?

2. What will the product price be in each market?

3. How much will be produced in each plant?

4. How much of the firmâs profit can be attributed to each plant?

Hint: The output from both plants can be sold in either market.

Part B: After the firm learns it is to be regulated to make a profit

equal only to a normal rate of return, it decides to consolidate

production into a single plant (but it will still sell in both markets).

After consolidation, total cost is represented by the equation:

TC = 8940 â 10Q + 0.75Q2,

where Q represents the total output produced in this single

(consildated) plant. Market demand is as described in Part A of this

problem. Given this information,

1. How much will this firm sell in each of the two markets?

2. What will the product price be in each market?

3. Are consumers better or worse off before or after the regulation?

If so, by how much?

Problem 2. Suppose the utility function of the average consumer of

gasoline is:

U = X0.15Y0.75

where X represents the number of gallons of gasoline purchased by this

person per week and Y represents the number of âunitsâ of all other

goods consumed by this person per week. If this personâs weekly

income is $300, then:

1. What is the per gallon price of gasoline if this person purchases

$50 worth of gas per week?

2. If a 50 per cent per gallon tax is imposed on gasoline, what would

be this personâs weekly, after tax consumption of gasoline?

3. How much would this person have to be reimbursed in order to make

him/her feel as well off as s/he did prior to imposition of the 50 per

cent per gallon tax?

4. If a 50 per cent per gallon tax is imposed on gasoline but the full

amount of the tax collected (on all gallons purchased) is rebated as a

cash payment to this person, what would be this personâs weekly

consumption of gasoline after (s)he receives the rebate?

5. What is the maximum amount this person would be willing to pay to

avoid the 50 per cent per gallon tax on gasoline?

6. If a 50 per cent per gallon tax is imposed on gasoline but the full

amount of the tax is rebated in the form of coupons that can be used to

purchase anything but gasoline, what would be this personâs daily

consumption of gasoline after (s)he receives the rebate?

PLEASE SEE ATTCHMENT

Problem 1.

Part A: A firm with âmarket powerâ is operating two plants and

selling its product in two markets. The demand and cost configurations

it faces are:

Demand: Costs:

Market 1: P = 484 â 20Q1 Plant 1: TC1 = 961 â 10 Q1 + EQ

QO(sdo4(1),sup4(2))

Market 2: P = 484 â 5Q2 Plant 2: TC2 = 324 â 10 Q2 +3 EQ

QO(sdo4(2),sup4(2))

On the demand side, Q1 represents the amounts sold in market 1 and Q2

represents the amounts sold in market 2. On the cost side. TC1

represents the total cost of producing Q1 level of output in plant 1

and TC2 represents the total cost of producing Q2 level of output in

plant 2.

Given the demand and cost figures above,

1. How much will this firm sell in each of the two markets?

2. What will the product price be in each market?

3. How much will be produced in each plant?

4. How much of the firmâs profit can be attributed to each plant?

Hint: The output from both plants can be sold in either market.

Part B: After the firm learns it is to be regulated to make a profit

equal only to a normal rate of return, it decides to consolidate

production into a single plant (but it will still sell in both markets).

After consolidation, total cost is represented by the equation:

TC = 8940 â 10Q + 0.75Q2,

where Q represents the total output produced in this single

(consildated) plant. Market demand is as described in Part A of this

problem. Given this information,

1. How much will this firm sell in each of the two markets?

2. What will the product price be in each market?

3. Are consumers better or worse off before or after the regulation?

If so, by how much?

Problem 2. Suppose the utility function of the average consumer of

gasoline is:

U = X0.15Y0.75

where X represents the number of gallons of gasoline purchased by this

person per week and Y represents the number of âunitsâ of all other

goods consumed by this person per week. If this personâs weekly

income is $300, then:

1. What is the per gallon price of gasoline if this person purchases

$50 worth of gas per week?

2. If a 50 per cent per gallon tax is imposed on gasoline, what would

be this personâs weekly, after tax consumption of gasoline?

3. How much would this person have to be reimbursed in order to make

him/her feel as well off as s/he did prior to imposition of the 50 per

cent per gallon tax?

4. If a 50 per cent per gallon tax is imposed on gasoline but the full

amount of the tax collected (on all gallons purchased) is rebated as a

cash payment to this person, what would be this personâs weekly

consumption of gasoline after (s)he receives the rebate?

5. What is the maximum amount this person would be willing to pay to

avoid the 50 per cent per gallon tax on gasoline?

6. If a 50 per cent per gallon tax is imposed on gasoline but the full

amount of the tax is rebated in the form of coupons that can be used to

purchase anything but gasoline, what would be this personâs daily

consumption of gasoline after (s)he receives the rebate?

## This question was asked on Apr 28, 2010.

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