[MATHEMATICS FOR ECONOMISTS] ASSIGNMENT 2.

[MATHEMATICS FOR
ECONOMISTS]
ASSIGNMENT 2
[DATE]

Question 1
1.1
1.2
1.3
1

1.4
1.5
2

1.6
Question 2
2.1 Function
At x = 1
Now,
Now,
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It can be seen that comes out to be positive and hence, it can be said that the function is
convex.
2.2 Demand function p = 100 - 0.01 x
Cost function C(x) = 50x +10000
2.2.1 Average cost function (AC)
2.2.2 Profit function (π)
Hence,
2.2.3 Value of x for which the profit is maximum
4

First derivative of profit function =0 (Maximum profit)
2.2.4 Maximum profit would be at x = 2500
2.2.5 Price for this level of production
p = 100 - 0.01 x
x = 2500
Question 3
3.1 Production function
Where,
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3.1.1 Marginal productivity of capital
Let
Now,
Marginal productivity of capital
Marginal productivity of labour
Let
Now,
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Marginal productivity of labour
3.1.2 MRTS of productions of shoes
MRTS when labour work hours L = 8 hours per day
Cost of capital K = 4
Now,
3.2 Implicit function
Differentiation w.r.t.x
7

Multiply both side with 2y
Hence,
Slope of the tangent line at (1,0)
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Question 4
4.1 Firm spends on fixed costs = $650
Total cost function =?
At
Hence,
4.2 Demand function
Marginal revenue
4.2.1 Change in TR when q has increased from 2025 to 2500
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4.2.2 The value of consumer surplus when q = 2500
Now,
4.3 Young’s theorem through
According to Young’s theorem, Z would be a valued function defined in such a way that both
the first order partial derivatives Z(x) and Z(y) would be differentiable and then,
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Proved!!
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