Mathmetical Economics
1) We are given a following production function, [pic]. a) Find out the MRTS. (6) b) Find out an expression for the expansion path. (2) c) What is the elasticity of substitution? (2)
2) Given a production function, Q=40K0.6L0.4 a) Find out the MRTS. (6) b) Find out an expression for the expansion path. (2) c) What is the elasticity of substitution? (2)
3) Evaluate the following integrals: a) [pic] (2) b)[pic] (3) c)[pic] (3) d)[pic] (4) e) ∫x2lnx2 f)[pic] (4) g)[pic] (3)
4) a) Given the Marginal Propensity to save, [pic] find out the Saving and consumption functions, where S=0 when income is 81. (Income =y) (2)
b) What is the present value of the income stream generating 3000 taka a year with a discount rate of 6% for 2 years. What is the value of a perpetuity with such characteristics? (2)
c) Under a Monopoly, the demand function is [pic] and Marginal Cost function is [pic]. Find out the Consumer Surplus. Why can’t we have a Producer Surplus in this case? (4)
5) a) Given the following demand and supply functions and assuming market clears at every point, find out the time path of price, P(t). [pic] and [pic] I) What is the market clearing price? (4)
II) Assuming market adjusts as a fraction of excess demand, find out the time path of price and also the intertemporal equilibrium price. (6)
b)[pic]Solve the following exact differential equation: [pic] (3) c) Using Bernoulli Linearization, solve the following differential equation: [pic] (3) d) Using the same equation, see whether the separable variable method gives the same result or not. (3)
e) Solve the following first order linear and verify its result: dy/dx+7y=7 where, y(0)=7
2) Given a production function, Q=40K0.6L0.4 a) Find out the MRTS. (6) b) Find out an expression for the expansion path. (2) c) What is the elasticity of substitution? (2)
3) Evaluate the following integrals: a) [pic] (2) b)[pic] (3) c)[pic] (3) d)[pic] (4) e) ∫x2lnx2 f)[pic] (4) g)[pic] (3)
4) a) Given the Marginal Propensity to save, [pic] find out the Saving and consumption functions, where S=0 when income is 81. (Income =y) (2)
b) What is the present value of the income stream generating 3000 taka a year with a discount rate of 6% for 2 years. What is the value of a perpetuity with such characteristics? (2)
c) Under a Monopoly, the demand function is [pic] and Marginal Cost function is [pic]. Find out the Consumer Surplus. Why can’t we have a Producer Surplus in this case? (4)
5) a) Given the following demand and supply functions and assuming market clears at every point, find out the time path of price, P(t). [pic] and [pic] I) What is the market clearing price? (4)
II) Assuming market adjusts as a fraction of excess demand, find out the time path of price and also the intertemporal equilibrium price. (6)
b)[pic]Solve the following exact differential equation: [pic] (3) c) Using Bernoulli Linearization, solve the following differential equation: [pic] (3) d) Using the same equation, see whether the separable variable method gives the same result or not. (3)
e) Solve the following first order linear and verify its result: dy/dx+7y=7 where, y(0)=7