a.
The partial derivatives of the function
a.
Answer to Problem 2.1P
The partial derivatives of the function
Explanation of Solution
Given information:
The function,
Since,
Partially differentiate with respect to x and y ,
and
Now
and
Also,
b.
The derivative
b.
Answer to Problem 2.1P
Explanation of Solution
Given information:
The function,
and
Since,
Then,
Differentiate with respect to x ,
c.
The value of
c.
Answer to Problem 2.1P
Explanation of Solution
Since,
Substituting
d.
To draw:The graph of
d.
Explanation of Solution
Since,
From the above part,
So, draw the tangent plane on the surface
Want to see more full solutions like this?
Chapter 2 Solutions
Microeconomic Theory
- 1. (question on photo) 2. How much income does the consumer have to spend on good x and y? 3. The partial derivative of Langrarian function with respect to good Y is one of the three first-order conditions that would have to hold in order for L to be maximized which could be written as?arrow_forwardThe variable shown on the vertical axis is _________ . The units for the variable on the horizontal axis are __________ . There are two ways to view the information presented on the graph. First, the graph tells us the amount a person with a certain income is likely to spend on a car, and second, it tells us the probable income of a person who spent a certain amount on a car. For example, if an individual earned $40,000 last year and purchased a new car, you would expect that person to have paid about _________ for the car. Similarly, if someone just paid $25,000 for a car, you could use this graph to estimate that this person's income was probably around __________ .arrow_forwardThe following table shows the quantity D of wheat, in billions of bushels, that wheat consumers are willing to purchase in a year at a price P, in dollars per bushel. D = quantity of wheat P = price 1.0 $2.05 1.5 $1.75 2.0 $1.45 2.5 $1.15 In economics, it is customary to plot D on the horizontal axis and P on the vertical axis, so we will think of D as a variable and of P as a function of D. (a) Show that these data can be modeled by a linear function. For each increase of 0.50 in D there is of in P. Find its formula. (Use P for price and D for quantity.)P = −.6d+265 (b) Add the graph of the linear formula you found in part (a), which is called the market demand curve, to the following graph based on the following table for market supply curve. S = quantity of wheat P = price 1.0 $1.35 1.5 $2.40 2.0 $3.45 2.5 $4.50arrow_forward
- Please find the effect of Y and r if there is a decrease in the tax rate. Use the following equations and evaluate the total derivative.arrow_forwardSuppose interest rate is 10 % and consumer's utility function is given by U(C1,C2)=C1C2. Income in the first period is 100 and income in the second period is 121. a) Find optimal consumption is each period. b) Does the consumer borrow? In which period? How much? c) Show the answers on a diagram.arrow_forwardSolve each of the following equations for x x+7=14 5x+4=24 12−4x=−20 Organize each of the following equations to express Pas a function of Q. QQ as a function of P PP as a function of Q Q=25−P Q=12−3P 6Q=14−2Parrow_forward
- Suppose that C = a + bY, where C = consumption, a = consumption at zero income, b = slope, and Y = income. a. Are C and Y positively related or are they negatively related? b. If graphed, would the curve for this equation slope upward or slope downward? c. Are the variables C and Y inversely related or directly related? d. What is the value of C if a = 10, b = 0.50, and Y = 200? e. What is the value of Y if C = 100, a = 10, and b = 0.25?arrow_forwardCome up with two variables that, in your view, are related, indicate the name of these variables as well as why these variables are related; determine which variable is the dependent variable and which one is the independent variable. Draw a line graph by hand, labeling the vertical and horizontal axis consistent with your choice of variables. The line in the line graph has to represent, what, in your view, is the relationship between the two variables. Describe your graph verbally in your post (no need to upload the graph itself). Note:- • Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. • Answer completely. • You will get up vote for sure.arrow_forward5. Suppose interest rates are zero and the consumer's utility is u(c_{1}, c_{2}) = (c_{1}, c_{2}) while the two incomes are (y_{1}, y_{2}) = (75, 125) . Find the optimal consumption in each period , and also indicate what financial transactions the consumer makes . Show the answers on a diagram .arrow_forward