Topic 4

Consumption according to Keynes

Consumption and Investment

一个例题

Ex. $Y=K^{0.3}{L}^{0.7},P_K=2,P=1,r=20\%,\delta =5\%,Y=100,K^{\ast }?$

Step: $Y=K^{0.3}{L}^{0.7}\to MPK=\frac{\delta Y}{\delta K}=0.3\frac{100}{K}$

When $MPK=\frac{P_K}{P}(r+\delta )$

So it is easy to calculate $K^{\ast }=60$

Since $K_{t+1}=(1-\delta )K_t+I_t=K_t-\delta K_t+I_t$

$\delta K_t$ refers to Depreciation of $K_t$

$K_{t+1}-K_t+\delta K_t=I_t$

If we assume $K_{t+1}=K^{\ast }$

Then, $I^{\ast }=I_t=K^{\ast }-K_t+\delta K_t$

Lets come to the previous question. What is $I^{\ast }$

Assume: $K_t=30$,

Because: $I^{\ast }=K^{\ast }-K_t+\delta K_t=31.5$

Why don’t need to calculate the labor cost?

The Stock Market & Tobin’s q

Stock (股票) - it refers to shares in the ownership of cooperation.

Stock Market (股票市场)--- It is the market where stock are traded.

To raise funding (集资…)：

Banks:

1. Bank-based (Eg. Germany)

2. Market - based (Eg. USA…)

ToBin’q = Market value (市值)of installed capital (e.g. assets of a firm)/Replacement cost of installed capital (e.g. assets of a firm)

What is replacement cost?

It is the price of capital if capital is purchased today!

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Example: ABC company has $40millionassets.Onemillionstocksareissuedandthepriceofthemis$3 per stock. Tobin’s q?

=\frac{1\ million * \ 3}{40\ million}=0.75<1$

If Tobin’s q > 1,

Managers should buy more capital

If Tobin’s q < 1,

Managers should stop buying more capital. They should not replace old capital

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If $MPK>\frac{P_K}{P}(r+\delta )$, firms make profit $\to$ The market value of the firm’s stock $\uparrow$ $\to$ Tobins’q $\uparrow$ Note that if they meet a loss, the result would be negative.

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Why stock prices and GDP move together?

Reason: When stock prices fall $\to$ Tobins’q $\downarrow$ $\to$ investors worry about the profitability $\to$ Investment $\downarrow$

2. Residential investment

It includes the purchases of new housing who plan to live in it and by landlords who plan to rent it out.