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Answer :
in a public open economy, the government has a role to play in the economy.
a) assuming that the full-employment level of output is $1000, there is a recessionary gap of $100. this is because the equilibrium level of output is $900, which is below the full-employment level of output
b) consumers are saving $100 at full employment. this is because disposable income is $1000 and consumption is $900.
c) the equilibrium value for a public open economy is $900. this is because the aggregate demand curve is equal to the aggregate supply curve at an output of $900.
d) the equilibrium for a private open economy is $800. this is because the aggregate demand curve is equal to the aggregate supply curve at an output of $800, without government spending.
e) the value of the multiplier is 5. this is because the equilibrium level of output increases by $5 for every $1 increase in government spending.
here is the solution in more detail:
a)the consumption function is c = 100 + 0.8yd, where c is consumption, yd is disposable income, and 0.8 is the marginal propensity to consume (mpc). the investment function is ig = 50. government spending is g = 60. exports are x = 120. imports are m = 190.
the full-employment level of output is $1000. this is the level of output at which all resources are fully employed.
the equilibrium level of output is the level of output at which aggregate demand is equal to aggregate supply.
aggregate demand is the total amount of goods and services that households, businesses, and governments want to buy at a given price level. aggregate supply is the total amount of goods and services that firms are willing to produce at a given price level
in this case, the aggregate demand curve is equal to the aggregate supply curve at an output of $900. this means that the equilibrium level of output is $900.
there is a recessionary gap of $100. this is because the full-employment level of output is $1000, but the equilibrium level of output is $900. the recessionary gap is the difference between the full-employment level of output and the equilibrium level of output.
b)at full employment, disposable income is $1000. consumption is $900. the government can use fiscal policy to increase aggregate demand. fiscal policy is the use of government spending and taxation to influence the economy.
in this case, the government can increase government spending by $100. this will increase aggregate demand by $100. the increase in aggregate demand will lead to an increase in output of $500. the equilibrium level of output will be $1400.
d)in a private open economy, the government does not have a role to play in the economy. the economy is left to its own devices.
in this case, the equilibrium level of output will be $800. this is because the aggregate demand curve is equal to the aggregate supply curve at an output of $800, without government spending.
e)the multiplier is the ratio of the change in output to the change in spending. in this case, the multiplier is 5. this is because the equilibrium level of output increases by $5 for every $1 increase in government spending.
the multiplier is greater than 1 because of the spending effect. the spending effect is the increase in aggregate demand that results from an increase in spending. the increase in spending leads to an increase in income, which leads to an increase in consumption, which leads to an increase in aggregate demand.
the multiplier is also greater than 1 because of the tax effect. the tax effect is the decrease in aggregate demand that results from an increase in taxes. the increase in taxes leads to a decrease in income, which leads to a decrease in consumption, which leads to a decrease in aggregate demand.
however, the multiplier is not infinite. the multiplier is smaller than infinity because of the saving effect. the saving effect is the decrease in aggregate demand that results from an increase in savings. the increase in savings lea
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