Consider the following mathematical representation of the Classical Model (or the loanable funds model) for a closed economy:
4)G and T are both fixed
8) The endowments of capital and labour are L and K , respectively (both are fixed)
a) What happens if the government increases government spending ( change in G) financed by a increase in taxes of equal size ( change in T). What is the overall effect on the interest rate and investment? Does your answer depend on the marginal propensity to consume?
b) What happens to total GDP and its components if the labour force is reduced?
Can you please tell me the answers, but more importantly, show me how to derrive them from the above information?
I have a problem with two of your stated conditions. I assume that 3 means that investment is a function of the interest rate, and that the 'R' in 8 stands for rate of interest. These assumptions lie behind my answers. I note also that the analysis is designed to be classical and not Keynesian, which would produce at least some different conclusions.
1. An increase in government spending is an injection into the circular flow of income. It will raise the level of income by an amount depending on the value of the multiplier, which in turn depends upon the value of the marginal propensity to consume. The increase in taxation is a withdrawal from the circular flow, and will reduce the level of income by an amount again depending on the value of the multiplier and thus the mpc. So, suppose G and T each rise by 1000 and the value of the mpc is 0.8. Then the value of the multiplier is 5. So the increase in G would raise income by 5000. The increase in T (also of 1000) will lower Y by 1000 in the first instance. Since the mpc is 0.8, this means that 800 comes from C and 200 from S. The reduction in C of 800 causes a fall in income of 800 x 5 (a downward multiplier effect) which is equal to 4000. Hence the net effect of the rise in G and equivalent rise in T is not neutral; rather it is to increase income by 5000 minus 4000 equals 1000 - in other words, the rise in income is equal to the rise in G and rise in T. This is known as the balanced budget multiplier theorem, which states that a tax-financed increase in G will raise income by an amount equal to itself. This is the case irrespective of the value of the mpc used in the calculation, so the value of the mpc does not affect the answer.
On a loanable funds (and not, I stress, a Keynesian) basis, the increase in income will increase the supply of loanable funds (savings). The result of the rightwards shift of the savings function is to lower the rate of interest, which in turn increases the demand for loanable funds (investment). So there is a movement along the investment function in order to restore equilibrium at a lower interest rate.
2. A reduction in the labour force will increase the price (wage) of labour. A smaller quantity of labour will be employed; hence its marginal product will rise, but its total product will fall. There will be some substitution of the now relatively cheaper capital for labour, which in turn will cause its price to rise. It is not possible from the information given to assess the degree of substitution, but it will continue to occur until the marginal product of labour divided by its price is equal to the marginal product of capital divided by its price. While in the long run new capital might become available (since the rate of return on it is now relatively greater), in the short run total output (GDP) in the economy should fall, as one of the two factors contributing to production has fallen in quantity (assuming no change in total factor productivity and also assuming that the increase in capital employed is insufficient to offset the fall in labour employed). At the same time, the wage paid to labour has risen (because of the shortage) and so the total wages earned by labour as a whole would rise so long as the demand for labour is price inelastic. Given the link between wages and consumer spending, it would be possible to argue that there is thus an injection into the circular flow, meaning that income (and thus output) would rise (though this is essentially a more Keynesian approach). This would be at least partly offset by any reduction in spending arising out of a fall in profits that is the result of both labour and capital now being more expensive.
I hope this is helpful.