Answer to Question #203112 in Microeconomics for Dhritabrata Paul

Question

FarFlung make computer keyboards. They use both labour, L, and materials, M, in their production of keyboards. The production method they use requires that at least one labour and one material is always employed. FarFlung have a Cobb-Douglas technology which means that their production function is: 𝑄(𝐿, 𝐾) = 𝐿𝑀.

(a) If fixed costs are £1000000 then what is the short run total cost of production and the short run average cost of production?

(b) FarFlung could move to a new factory, where they will be able to manufacture 360000 computer keyboards. They are confident they can sell all the keyboards, but they will need to reduce price from £20 to £10. Whilst they will be able to use the same technology, the fixed costs will increase to £2000000.

i. What is the new level of short run average costs? What does this imply about the shape of the long run average cost curve?

ii. Should FarFlung move to the new plant? Explain. (c) What could FarFlung do to decrease their costs?

Answer 1

Given

$Q = LM\\ Q = 160,000\\$

$MPL = \frac{dQ}{dL }= M\\$

$MPM = \frac{dQ}{dM} = L\\$

a)

Fixed costs (FC) = £1000000

price of labor is £100 and the price of materials is £25

Price ratio$= \frac{100}{25} =4$

The slope of the isoquant curve equals to the slope of isocost curve to the cost-minimization:

$\frac{MPL}{MPM} = \frac{PL}{PM}\\$

$\frac{M}{L} = 4\\ M = 4L-------------------------1$

Putting M=4L in production function:

Q = 4L²

4L² =160000

L = 200 units

Putting this in equation 1:

$M= 4\times200$ = 800 units

The cost function will be fixed cost + variable cost:

C = 1,000,000 + 100L + 25M----------------------2

$C = 1000000 + (100 \times200)+ (25\times800)$

C= £1,040,000

Average cost$(AC) = \frac{1,040,000}{160000}$

AC =£6.5 

b)i

The cost function will be fixed cost + variable cost:

C1 = 1,000,000 + 100L + 25M

Putting new L and M:

$C1 = 2000000 + (100 \times 300) +(25\times1200)$

C1= £2,060,000

Average cost $(AC) =\frac{ 2,060,000}{360000}$

AC1 = £5.72 

As the AC reduces as the quantity increases. The long-run average cost is downward sloping.

b)ii

The initial price with quantity Q=160000 is £20

The price after an increase in quantity from Q to Q1=360,000 is £10

Initial Total Revenue$(TR) = 160000 \times 20 = 3,200,000$

Thus, Initial profit = TR-C = 3,200,000 - 1,040,000

Profit = £ 2,160,000

After quantity increased to Q1 = 360000, the price = £10

Total Revenue $(TR1) = 360000 \times 10 = 3,600,000$

Thus, profit1 = TR1-C = 3,600,000 - 2,060,000

Profit 1= £ 1,540,000

 the profit has reduced. So, the firm Farflung should not have moved to the new plant.

c)

Farflung can reduce their costs by;

1. Minimizing expenditure spend on utilities.
2. Taking advantage of technology.
3. Outsourcing business processes.
4. Cutting down on office space.
5. Employee perks.