Ec 10 Fall 2006 Pset 4

Tarun Singh TF: Andres Zahler November 6, 2006 Ec 10- Problem Set 4 1. A) Their total economic costs of running the business over the year would be: TC= Pat Salary + Chris Salary + lost interest on Pat’s investment + interest paid on Chris’ investment + cost of machinery + cost of ingredients + salary paid to workers + rent. TC= $40,000 + $40,000 + ($10,000 x .04) + ($5,000 x .10) + $20,000 + $10,000 + $20,000 + ($1,000 x 12) TC= $142,900 B) To have zero accounting profit they would need a total revenue that is equal to the total explicit costs. In this case, explicit costs are equal to ($500, + $20,000 + $10,000 + $20,000 + ($1,000 x 12)) which equals $62,500. To have zero economic profit they would need a total revenue that is equal to the total economic costs which was calculated in part A to be $157,900. These revenues are different because economic profit includes the firm’s explicit and implicit opportunity costs, whereas accounting profit only includes the firm’s explicit opportunity costs. C) The costs of machinery (i), salary (iii), and rent (iv) are fixed costs and the cost of ingredients is variable (ii) in the short run, because only the cost of ingredients will depend on demand the rest of the costs will be the same regardless of production. In the short run, the iii and iv are sunk costs because they have already been committed and con not be recovered in full or in part.

2. # of workers 0 1 2 3 4 5 6 7

Output (Candelbras) 0 20 50 90 120 140 150 155

Marginal Product of Labor

Total Cost

Average Total Cost

Average Variable Cost

Marginal Cost

(Candelbra/worker)

$

$/Candelbra

$/Candelbra

$/Candelbra

20 30 40 30 20 10 5

200 300 400 500 600 700 800 900

15 8 5.56 5 5 5.33 5.81

5 4 3.33 3.33 3.57 4 4.52

A) The units of Marginal Product of Labor would be Candelbras. The Marginal Product of Labor initially increases but then starts to decrease. This can be attributed to the property of diminishing marginal product; initially when only a few workers are hired the workers have easy access to necessary materials and equipment but as the number of workers hired increases additional workers have to share resources and start to get in each others’ ways, thus making each additional worker contribute less. B) Total Cost rises as quantity increases, Average Total Cost decreases as quantity is increased, while Marginal Cost and Average Variable Cost both decrease at first but then increase. Total Cost rises because it costs more to hire each additional worker, but Average Total Cost falls because the initial fixed cost is spread out over a higher quantity. C) Marginal Product of Labor and Marginal Cost increase and decrease with each other and are proportional to each other in this case. For example every time MPL is 20 the MC is 5 and every time MPL is 30 the MC is 3.33 etc. This correlation is because both MPL and MC measure efficiency in a way. MPL measures how many more units an additional worker can produce and MC measures the cost of an additional unit, thus the additional cost of an additional unit is based on MPL and it makes sense for the two curves to correlate.

5 3.33 2.5 3.33 5 10 20

3. She should not make one more dose because the marginal cost of producing the 201st dose is greater than the price that the customer is offering. Marginal cost is found by using: (ΔTC/Δq) which is equal to (((ATCq=201 x q) – (ATCq=200 x q))/Δq) which is ((201 x 201) – (200 x 200)/1) = $401 Thus the cost is $401 for the 201st unit whereas the price the consumer is paying for that unit is only $300.

4.

A) TC= 10 + 10q + q2, ATC= (10 + 10q + q2)/q, AVC = (10q + q2)/q= 10 + q, MC= 10 + 2q. Average Variable Cost is a linear function; it has a constant slope. As “q” increases AVC increases, and as “q” decreases AVC decreases. The graph of AVC is not U-shaped. ATC is U-shaped; it is a quadratic function and therefore follows a Ushaped curve. B) To reach maximum profit in the short run the firm must produce where Marginal Cost is equal to Price. MC= 10 + 2q Price= P 10 + 2q=P 2q= P – 10 q= .5P - 5 C) Q= 12(q) = 12(.5P - 5) Q= 6P - 60 D) Demand= 100 – 2P, Supply = 6P – 60 Equilibrium Point for this industry is where Demand=Supply 100 – 2P=6P – 60 P= 20 Q=100 – 2(20) = 60 Each individual firm produces Q/12 which is 60/12 which is 5 units. Profits for each individual firm = q(P – ATC) ATC= (10+50+25)/5=17 Profit=5(20-17) = $15 Each firm makes a profit of $15 This is short run equilibrium. In long run, there are no economic profits. If economic profits exist firms will enter the market thus causing the price to go down which will eventually lead to zero economic profits

E) Assumption: In the long run there will be no economic profit and firms will have joined the market decreasing the overall price of the good so MC=ATC (q/1)(10 + 2q)= ((10 + 10q + q2)/q)(q/1)

10q + 2q2= 10 + 10q + q2 q2= 10 q= 10 P= 10 + 2q = 10 + 2 10 Long run individual output: 10 and Long run equilibrium price: 10 + 2 10 QD= 100 – 2(10 + 2 10 ) = 100 – 20 – 4 10 = 80 - 4 10 : this is the industry Long run # of firms= (total output)/ (individual output)= (80 - 4 10 )/ 10 Long run # of firms= 8 10 - 4

5. A)

B)

Supply of pretzels in the city will shift to the left since there are fewer suppliers, thus increasing the price. The individual stands now operating will see a profit in the short run because the new price is above the point where MC and ATC cross. C) The selling of license fees will increase ATC because the license fee is an increase in fixed cost. However, the quantity of pretzels sold will not change unless the lowest point of ATC rises above the price in which case an individual firm may shut down temporarily. The price of pretzels in the city should not change as a result of the fee. D) The city should institute a license fee that is equal to the distance between the new and old price because this would raise the lowest point of ATC to the new price, which is the highest the nadir of ATC can be without causing firms to stop producing.

6. A) Let’s assume that the fixed costs of a burger producer before tax are $1.00 and that the producer can produce burgers with costs outlined below. Doing so we can institute the lump sum tax of $300 and see what effects would occur # of Burgers

Fixed Costs ($)

0.00 1.00 2.00 3.00

1.00 1.00 1.00 1.00

Average Variable Cost

Fixed Costs After Tax ($) 301.00 301.00 301.00 301.00

Total Cost ($) 1.00 3.00 5.00 6.00

Marginal Cost

AVC After Tax ($/Burger)

($/Burger) 0.00 2.00 2.00 1.67

Total Cost After Tax ($) 301.00 303.00 305.00 306.00

($/Burger) 0.00 2.00 2.00 1.67

Average Total Cost ($/Burger)

Average Total Cost After Tax ($/Burger)

3.00 2.50 2.00

303.00 152.50 152.00

Marginal Cost After Tax ($/Burger)

2.00 2.00 1.00

2.00 2.00 1.00

(Note the graphs will not represent the numbers from the table, since the numbers are just there to help clarify the concepts)

Looking at the data we can see that ATC increases, but AVC and MC stay the same. This is because an increase in fixed costs increases the total costs but has no effect on variable cost and since variable cost is unchanged, MC is also unchanged by the tax. B) Using the same assumptions form part A) let us impose a tax of $1 per burger and see what happens. # of Burgers

Fixed Costs ($)

0.00

1.00

Fixed Costs After Tax ($) 1.00

Total Cost ($) 1.00

Total Cost After Tax ($) 1.00

Average Total Cost ($/Burger)

Average Total Cost After Tax ($/Burger)

1.00 2.00 3.00

1.00 1.00 1.00

Average Variable Cost ($/Burger) 0.00 2.00 2.00 1.67

1.00 1.00 1.00

3.00 5.00 6.00

4.00 6.00 7.00

Marginal Cost

AVC After Tax ($/Burger)

($/Burger) 0.00 3.00 2.50 2.00

2.00 2.00 1.00

3.00 2.50 2.00

Marginal Cost After Tax ($/Burger) 2.00 2.00 1.00

(Note the graphs will not represent the numbers from the table, since the numbers are just there to help clarify the concepts)

With a tax of $1 per burger, ATC increases, AVC increases but MC does not change. A tax of $1 per burger changes AVC because the tax is based on how many burgers are sold thus changing the variable cost. Since total cost is just fixed cost + variable cost, total cost is also increased by an increase in variable cost. MC is not changed because the difference between the cost of each additional burger is not changed because each burger costs $1 more than before.

4.00 3.00 2.33