Loanable funds theory and Keynes’s liquidity preference theory

The Loanable funds theory Hypotheses: Individuals care only about real variables (output gains or losses, purchasing-power gains or losses). The marginal productivity of capital assets (MPK) is given and determined by the technical characteristics of the productive assets. It represents the gain, in terms of output, obtained by increasing the capacity of production by one additional capital asset. The higher the MPK, the higher the real interest has to be not to give the incentive to invest. The time preference of individuals (t) is given by the taste of individuals. It represents the impatience of individuals: what individuals are ready to give up today, in terms of output, in order to consume more in the future. The higher their time preference (people do not like to save), the higher the real interest rate (the reward) must be in order to give the incentive to save. Entrepreneurs want to maximize their real profit Π/p = q(K, N) – wN – rK, with w the real wage and r the real rate of interest. In order to do so, they must determine the amount of N and the amount of K which are given by: d(Π/p)/dN = 0 ⇒ q’(N) = w ⇔ MPL = w: demand for labor. d(Π/p)/dK = 0 ⇒ q’(K) = r ⇔ MPK = r: demand for capital. Individuals want to maximize their utility by arbitraging between present consumption and future consumption (and so saving): U(C0, C1). They do so under the constraint of their intertemporal budget constraint: R0 + R1/(1 + r) = C0 + C1/(1 + r) with R the real income, and r the real rate of interest. The level of C0 and C1 are determined by (λ is the factor attached to the budget constraint in the Lagrangian): dl/dC0 = 0 ⇒ U’(C0) = λ dl/dC1 = 0 ⇒ U’(C1)×(1 + r) = λ U’(C0)/U’(C1) = 1 + r ⇔ 1 + t = 1 + r dl/dλ = 0