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# 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...

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!!!

Problem 1.
Part A: A firm with âmarket 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 firmâs 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 âunitsâ of all other
goods consumed by this person per week. If this personâs 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 personâs 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 personâs 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 personâs daily
consumption of gasoline after (s)he receives the rebate?

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