hw5 - IS − LM model is Y = C Y M P I r G M/P = L Y r Note...

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ECONOMICS 331 Mathematical Economics Kevin Wainwright Homework Assignment 5 1. Consider the f rm with a single factor of production de f ned implicitly by the relation z = q 3 +4 q where z is the variable input and q is output. The f rm faces the following average revenue function: p =10 2 q Calculate the point elasticity of the f rm’s total sales revenue with respect to the amount of labour used when q =2 . 2. The following three equations de f ne x, y ,and w as functions of z. xy w =0 y = w 3 +3 z w 3 + z 3 =2 wz Find an expression for x/ z andeva luateitatthepo intwhere w = z =1 3. The equation x 2 + y 2 + z 2 + xy + xz + yz + x + y + z 1=0 has one solution ( x, y, z )=(1 , 1 , 1) . Checktha ttheequat iondoesindeedde f ne z as a function of x and y at this point. Calculate the partial derivatives of z with respect to x
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Unformatted text preview: IS − LM model is Y = C ( Y, M P ) + I ( r ) + G M /P = L ( Y, r ) Note that the term, M P appears in the consumption function. This what is sometimes referred to as the Real Balances E f ect. (a) Make a sensible assumption about the sign of ∂ C/ ∂ ( M P ) ? Justifying your assump-tion (only your f rst sentence will be read). (b) Setup and sign the Jacobian of this system. (c) Determine the comparitive static results about how changes in M a f ect Y and r. Use the normal economic assumptions about the derivatives of, I ( r ) and L ( Y, r ) . (d) Redo (c) except this time let P be the exogenous variable that in F uences Y and r (remember to use the chain rule). 1...
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