Part a) The Cob Douglas production function is given as:
To show that this function is homogeneous with degree 3, we introduce be a parameter, t.
Using properties of exponents, we on tinder:
This implies that:
Simplify the exponent of t to get;
Hence the function is homogeneous with degree, 3
Part b) To verify Euler's Theorem, we must show that:
Verifying from the left:
Q•E•D
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Answer: Option (A) is correct.
Explanation:
In a competitive market, when the demand curve i.e. the marginal benefit curve is exactly equal to the supply curve i.e. marginal cost curve and at this point the sum of consumer and producer surplus is maximized then an equilibrium is set in an economy and economic efficiency is obtained.
Inefficiency occurs at a point where there is a disequilibrium in an economy which means that competitive equilibrium is not achieved by the economy.
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