Question

Consider a corn farm, a bakery, some consumers and a government.

The corn farm grows 4 million tons of corn and the market price of corn is $50/ton. 1.5 million tons of corn are sold to consumers and the government buys 1 million tons to feed the army. The bakery buys 0.5 million tons of corn and sells it as cornbread to the consumers, earning a revenue of $50 million. The remaining 1 million tons are stored as inventory.

The corn farm pays $40 million in wages, $30 million on renting machinery and $45 million in taxes to the government. The bakery uses no additional inputs and pays $10 million in taxes. Consumers pay $10 million in taxes and receive $15 million in government transfers through a pension plan. The profits of the corn farm and bakery are distributed to the consumers.

Calculate GDP using all three methods: value added (production), expenditure, and income approach.

Answer 1

Solution:

Expenditure approach:

GDP = C + I + G + NX ; where C is consumption, I is investment, G is the government expenditure, and NX is the net exports. Since, we do not deal with the trade among other nation here, NX directly goes to 0 for such closed economy model.

Government expenditure involves the purchase of 1 million ton it makes to corn farm. So, G = 50*1 million = $50m

We find the net government expenditure as net of taxes paid by firms, So, net G = 50 - 45 - 10 = -$5m

Investment includes the inventory amount, I = 50*1m = $50m

Consumption is what the final consumers spend, net of what they have to pay as taxes and receive as revenue. Consumption expenditure = 50*1.5m (corn farm) + $50m (bakery) = 75m + 50m = $125m

So, C = consumption exp - T + TR; T is taxes consumer pay, and TR is the transfer they receive from government,

C = 125 - 10 + 15 = $130m

So, GDP = 130m + (-5m) + 50m = $175m

Income approach:

Revenue for corn farm = 50*3m= $150m (since inventory of 1m is not sold), while it bears the cost = wage + machine rent = 40m + 30m = $70m

So, profit for corn farm = 150m - 70m = $80m

Similarly, revenue for bakery firm as given = $50m ; cost = 50*0.5m (input cost) = $25m

So, profit of bakery firm = 50 - 25 = $25m

GDP = wages + capital rent + dividend + profit

GDP = $40m + $30m + 0 + ($80m + $25m) = $175m

Value added approach:

It is simply the value of final goods, directly used for consumption. So, corn farm sells 2.5 millions of it (1.5m to consumers, 1m to government for army). Note that bakery selling of 1m will not be counted as it will result in double counting.

Bakery sells $50m worth cornbread

So, GDP = 50*2.5m + 50 = $175m