I need help with this homeowrk question i am unsure if i have it correct. Suppose a consumer’s utility function is given by U(X,Y) = X^1/2*Y^1/2. Also, the consumer has $36 to spend, and the price of good X is P(x) = $4. Let good Y be a “composite” good (good Y is the “numeraire”) whose price is P(y) = $1. So, on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X. if P(x) increases to 9 and the new bundle of the customers demands are 2 units of x and 18 units of y, how much additional money would the consumer need in order to have the same utility level after the price change as before the price change? (Note: this amount of additional money is called the Compensating Variation.) and of the total change in the quantity demanded of good X, how much is due to the substitution effect and how much is due to the income effect? (Note: since there is an increase in the price of good X, these values will be negative)
I need help with this homeowrk question i am unsure if i have it correct.
Suppose a consumer’s utility function is given by U(X,Y) = X^1/2*Y^1/2. Also, the consumer has $36 to spend, and the price of good X is P(x) = $4. Let good Y be a “composite” good (good Y is the “numeraire”) whose price is P(y) = $1. So, on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X.
if P(x) increases to 9 and the new bundle of the customers demands are 2 units of x and 18 units of y, how much additional money would the consumer need in order to have the same utility level after the price change as before the price change? (Note: this amount of additional money is called the Compensating Variation.) and of the total change in the quantity demanded of good X, how much is due to the substitution effect and how much is due to the income effect? (Note: since there is an increase in the price of good X, these values will be negative).
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Draw on a graph the
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original budget constraint (draw this in black)
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new budget constraint (draw this in green)
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compensated budget constraint (draw this in red)
Also, on your graph, indicate the optimal bundle on each budget constraint.
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Label the optimal bundle on the original budget constraint X* and Y*
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Label the optimal bundle on the new budget constraint X** and Y**
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Label the optimal bundle on the compensated budget constraint XC and YC
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graph must be neat, accurate, and fully labeled. Make sure to label each budget constraint with the correct values of M, PX, and PY. Also make sure to identify the correct values of X and Y in each bundle. (Do not scale the Y-axis above 60, and do not scale the X-axis above 12.)
i need help in terms od graphing this
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