You are given the following supply and demand curve functions for a market
Eco 70
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Instructions: This will count for 60 pts on your final exam. Responses must be submitted prior to receiving the exam on May 13th. The question has multiple portions and each piece builds on the next section. Be prepared to answer this information as you proceed to the next portion. SHOW ALL YOUR WORK! GRAPHS, FORMULAS, MATH, EVERYTHING!
1.) You are given the following supply and demand curve functions for a market for sunglasses.
Q_D=-2(P)+340
Q_S=5P-150
Graph the following:
The demand curve;
The supply curve;
Consumer surplus
Producer surplus;
Total surplus;
The equilibrium price and quantity; and,
Total revenue for this market.
Using the functions above, the following table is found. Please complete this table.
Price Quantity Sold Quantity Produced Total Revenue Fixed Cost Variable Cost Total Cost Marginal Cost Average Total Cost Average Fixed Cost Average Variable Cost Profit Marginal Revenue
$0 340 0 $0 $150 $0 $150 – – – – – –
$40 260 50 $10,400 $150 $140 $290 $2.80 $5.80 $3.00 $2.80 $10,110 -$130
$50 240 100 $12,000 $150 $260 $310 $0.40 $3.10 $1.50 $1.60 $11,110 $80
$60 220 150 $13,200 $150 $210 $360 $1.00 $2.40 S1.00 $1.40 $12,840 $60
$70 200 200 $14,000 $150 $330 $480 $2.40 $2.40 $0.75 $1.65 $13,520 -$40
$100 140 350 $14,000 $150 $710 $ 860 $2.53 $2.46 $0.43 $2.03 13,140 $0
$120 100 450 $12,000 $150 $970 $1,120 $2.60 $2.49 $0.33 $2.16 $10,880 $50
Please graph the following using the previous table:
Marginal cost;
Average total cost;
Average fixed cost;
Marginal revenue; and,
Average variable cost.
2.) If a price ceiling of $100 is imposed, what will happen within this market? Please graph the results and explain.
A: At the $100 ceiling would reduce the demand level and increase the supply level of the sunglasses.
3.) Suppose a consumer report comes out stating that sunglasses will decrease the risk of cataracts by 20 percent if worn during peak sun hours regularly. What may happen in the market for sunglasses? Please draw and explain the change in the graph. Using the previous table, select a new price and quantity supplied. You know Qs = Qd at equilibrium, so if you are looking for:
Q_d= -2P+x
A:The demand and supply for the sunglasses would increase and so would the price.
QD= -2(P)+408 QS=5P-180
Price QS QD QS
$10 -2 408 388 $3,880 $10 5 -180 $(130)
$50 -2 408 308 $15,400 $50 5 -180 $70
$60 -2 408 288 $17,280 $60 5 -180 $120
$70 -2 408 268 $18,760 $70 5 -180 $170
$80 -2 408 248 $19,840 $80 5 -180 $220
$110 -2 408 188 $20,680 $110 5 -180 $370
$130 -2 408 148 $19,240 $130 5 -180 $470
Graph the following:
The original supply curve;
The original demand curve;
The original price at equilibrium;
The original quantity at equilibrium;
The new demand curve;
The new price at equilibrium;
The new quantity at equilibrium;
The original consumer surplus;
The new consumer surplus;
The original producer surplus;
The new producer surplus;
The original total surplus;
The new total surplus.
What is the change in total revenue under the new demand?
A:It would shrink the producer and consumer surplus,Total Revenue would increase from $75,600 to $115,080
4.) What happens if a $7 tax is imposed on sunglasses, find the equation for Q_STax. Solve for the following items:
The price buyers pay under the tax;
The quantity buyers will purchase at the price under the tax;
The price sellers receive under the tax for that quantity;
The new producer surplus under tax;
The new consumer surplus under tax;
The new tax revenue received;
The new total surplus under tax; and,
The deadweight loss.
Use the new demand function found in Question 3 to solve as your Qd function. Please be sure to graph everything as well.
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