Question

1. Consider the typical individual in Fisher’s two-period model, who chooses between current and future consumption (C₁ and C₂) to maximize utility. Their preferences are such that the substitution effect dominates the income effect and savings increases when the interest rate rises.

1.   Draw the intertemporal budget constraint and indifference curve for this individual saver when
   r = 0.10. Label the utility-maximizing point by A. Which is greater, the marginal utility C₁ or the marginal utility of C₂? How do you know?
2.    Draw a loanable funds market and illustrate the equilibrium by point A. Suppose that shifting demographics cause the number of individual savers to fall. Label the new equilibrium after the demographic shift by point B. What happens to the level of aggregate savings, aggregate investment and the interest rate?
3.   Illustrate point B in your diagram for the individual saver. Explain how the adjustment to market equilibrium affects his/her behavior.   

Answer 1

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as the figure below gives the intertemporal budget constraint, Bobo as que : Vote The slope of the line is all. At equilibrium slope of ic is equal to all, the slope of Bl. The point E in the endowment or no borrowing no lending point (NIB/NL) or at E (4=Y) and ( 9 92). A is at the left of E giving the tact .a y, or the consumer is a saver. Figure 1 ---- BiBoa Gay-G b) ,S,SC) 50-56) At point A, muca) i :. Mu(a)=11 MUCE) müca " In other words, muca)> MUCCz) . Then at A greater than marginal marginal utility of a in utility of Ca. Figure - 2 The figure gives the loanable funds market. The demand for loan in the firm's 02 investment demand of and supply of funds is the national savings. D=1(Y) The equilibrium occurs at A, with interest - 4 Lo rate rool and total savings Lo. As the number of savers fan ; the national

savings shift to the left. The market moved along I (") increasing rate of interest r,= 0.2 and total decreasing investment to ti. Then as result aggregate sarking and investment falls at new equilibrium. c. In case of individual saver, a rise in interest increases savings. This implies at the increased interest rate a falls. Refering to figure I above, a rise in interest rate pirots the budget line clockwise around E, to Bibl. The new equilibrium occurs at B. At B , a falls to a< c. and a rises to c> c . Then as the market equilibrium increases r; sulestitution effect from rise in rar, which is negative and decreases as domi nates income effect of rise in ce. At new equilibrium a falls and savings (9,-6) nises al though the tool aggregate savings falls due to fall in number of savees.