Economics Tutorial 6

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Values when w1 = w2 = 1: ; ; total cost = [pic 40][pic 41][pic 42]

Can check what happens when this values change…

- Geetha sells milkshakes in a competitive market on a corner of Buchanan street. Her production function is where output is measured in gallons, x1 is the containers of ice cream which is used and x2hours of labour hours spent to produce the milkshake. [pic 43]

- What can you say about the returns to scale of the production function?

- Where w1 is the price of a container of ice cream and w2 is the wage rate for milk shake maker write down the iso-cost function for cost C.

- Define and find the marginal product.

- Geetha estimates that she would be able to sell Y gallons of milkshakes. Calculate the production plan which would enable her to produce this amount in the cheapest way and the associated cost.

- Discuss what would happen to the production plan in (d) when there is an increase in (i) w1, (ii) w2 and (iii) y.

is [pic 44]

- If we increase all the inputs by a proportion k:

[pic 45]

So it shows decreasing returns to scale.

-

which is the iso-cost line[pic 46]

Slope of the isocost function is –w1/w2

MP1 = (1/3)[pic 47]

MP2 = (1/3)[pic 48]

Technical rate of substitution=[pic 49]

At the cheapest input bundle to produce y units, the slope of the isoquant is equal to the slope of the isocost line (production function and iso-cost will be tangent to each other).

➔ x2=w1x1/w2[pic 50]

Substituting in production function, ➔ y=x12/3(w1/w2) 1/3[pic 51]

- X12/3 = y(w2/w1)1/3➔= x1* = w2½ y 3/2 / w1 ½

-

Substitute into x2=w1x1/w2➔x2=(w1/w2)w2½ y 3/2 / w1 ½

x2* = w1½ y 3/2 / w2 ½

c* = w1x1* + w2x2*

c* = 2w1 ½ w2 ½y 3/2

Carry out some comparative statics using calculus and intuition.