Given labour demand=c-dw
Labour supply=a+bw
A)determine equilibrium w
B)assume that a worker derive a benefit k in monetary value from government mandate to increase w by t
Labour demand=c-d(w+t)
Labour supply=a+b(w+k) find a)new w
b)what is the effect of k=0 on labour supply side (i,e:on workers)
A) To determine the equilibrium wage (w), we need to set the labour demand equal to the labour supply:
c - d(w) = a + b(w)
Next, we will solve for w:
c - a = (b + d)w
w = (c - a)/(b + d)
B) If a worker derives a benefit k from a government mandate to increase the wage by t, the new labour demand would be:
Labour demand = c - d(w + t)
Labour supply = a + b(w + k)
To find the new wage (new w), we set the new labour demand equal to the labour supply:
c - d(w + t) = a + b(w + k)
Next, we solve for new w:
c - a = (b + d)w + (bk - dt)
new w = (c - a - bk + dt)/(b + d)
B) If k = 0, meaning there is no benefit for workers, the labour supply would be:
Labour supply = a + b(w + 0) = a + bw
In this case, the effect on the labour supply side (i.e., on workers) is that there is no additional benefit or increase in the wage caused by a government mandate.
A) To determine the equilibrium wage (w), we need to equate the labor demand and supply equations and solve for w.
Equating labor demand and supply:
c - dw = a + bw
Rearranging the equation:
bw - dw = a - c
Factoring out w:
w(b - d) = a - c
Dividing both sides by (b - d):
w = (a - c) / (b - d)
Therefore, the equilibrium wage (w) is (a - c) / (b - d).
B) Assuming a worker derives a benefit (k) in monetary value from a government mandate to increase w by (t), we need to adjust both labor demand and supply equations by incorporating this benefit.
Adjusted labor demand equation:
c - d(w + t)
Adjusted labor supply equation:
a + b(w + k)
A) To find the new equilibrium wage (w), we equate the adjusted labor demand and supply equations and solve for w.
Equating adjusted labor demand and supply:
c - d(w + t) = a + b(w + k)
Rearranging the equation:
c - d(w + t) - a - b(w + k) = 0
Expanding and simplifying the equation:
c - dw - dt - a - bw - bk = 0
Rearranging and grouping terms:
w(b - d) = a + c - bk - dt
Dividing both sides by (b - d):
w = (a + c - bk - dt) / (b - d)
Therefore, the new equilibrium wage (w) is (a + c - bk - dt) / (b - d).
B) The effect of k = 0 on the labor supply side (i.e., workers) means that the worker does not receive any benefit from the government mandate to increase w by (t).
The adjusted labor supply equation when k = 0:
a + b(w + 0)
a + bw
In this case, the labor supply equation remains unaffected, meaning workers do not receive any additional benefit from the government mandate.
A) To determine the equilibrium wage rate (w), we need to set the labor demand equal to the labor supply and solve for w.
Labor Demand: c - dw
Labor Supply: a + bw
Setting them equal:
c - dw = a + bw
Now, let's solve for w.
Step 1: Move all the terms that include w on one side of the equation:
- dw - bw = a - c
Step 2: Factor out w:
w(-d - b) = a - c
Step 3: Solve for w by dividing both sides of the equation by (-d - b):
w = (a - c) / (-d - b)
Therefore, the equilibrium wage rate (w) is (a - c) / (-d - b).
B) Now, let's assume that a worker derives a benefit (k) in monetary value from a government mandate to increase w by t. This means the new labor demand and labor supply equations will be as follows:
New Labor Demand: c - d(w + t)
New Labor Supply: a + b(w + k)
To find the new equilibrium wage rate (new w), we need to set the new labor demand equal to the new labor supply and solve for new w.
c - d(w + t) = a + b(w + k)
Now, let's solve for new w following the same steps as in part A.
Step 1: Expand the brackets:
c - dw - dt = a + bw + bk
Step 2: Move all the terms that include w on one side of the equation:
- dw - bw = a - c + dt - bk
Step 3: Factor out w:
w(-d - b) = (a - c) + (dt - bk)
Step 4: Solve for w by dividing both sides of the equation by (-d - b):
new w = [(a - c) + (dt - bk)] / (-d - b)
Therefore, the new equilibrium wage rate (new w) is [(a - c) + (dt - bk)] / (-d - b).
B) When k = 0, i.e., there is no benefit to workers from the government mandate to increase w, the new labor supply equation becomes:
New Labor Supply: a + bw
In this case, the labor supply side (i.e., workers) is not affected by the value of k, as it does not exist. The equation is unchanged from the original labor supply equation.
Hence, when k = 0, there is no effect on the labor supply side (i.e., workers).